abstract booklet - msu.ru · 2015. 9. 13. · plamen ch. ivanov physics department, boston...

Nonlinear Dynamics of Electronic Systems (NDES) 2015

Como, Italy. Sept. 7-11, 2015

Abstract Booklet

Organizers:

Prof. Dr. Guilio Casati, ComoProf. Dr. Giorgio Mantica, ComoProf. Dr. Ruedi Stoop, Zurich

Prof. Dr. Sebastiano Stramaglia, Bari

Plenary talks

On global stability of delayed and non-delayed networks

Leonid BunimovichGeorgia Institute of Technology, Atlanta, USA.

We show that for a large class of time delayed networks their global stability follows from global stabilityof non-delayed networks. This result is surprising and allows to simplify analysis of dynamics of some timedelayed networks.

10:30-11:15, Monday 7 September.

Symmetries, cluster synchronization, and isolated desynchronization in complexnetworks

Lou PecoraUS Naval Res. Labs, Washington DC, USA.

Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predictthese clusters in general or understand the conditions for their formation. We show the intimate connectionbetween network symmetry and cluster synchronization. We apply computational group theory to revealthe clusters and determine their stability. In complex networks the symmetries can number in the millions,billions, and more. The connection between symmetry and cluster synchronization is experimentally exploredusing an electro-optic network. We observe and explain a surprising and common phenomenon (isolateddesynchronization) in which some clusters lose synchrony while leaving others connected to them synchronized.We show the isolated desynchronization is intimately related to the decomposition of the group of symmetriesinto subgroups. The results could guide the design of new power grid systems or lead to new understanding ofthe dynamical behavior of networks ranging from neural to social.


Chemobrionics: Nonlinear dynamics, electronic systems, and the origin of life

Julyan CartwrightUniversity of Granada, Spain

Chemical gardens are perhaps the best example in chemistry of a self-organizing nonequilibrium processthat creates complex structures. Many different chemical systems and materials can form these self-assemblingstructures, which span at least eight orders of magnitude in size, from nanometers to meters. Key to this magicis the self-propagation under fluid advection of reaction zones forming semipermeable precipitation membranesthat maintain steep concentration gradients, with osmosis and buoyancy as the driving forces for fluid flow.Chemical gardens have been studied from the alchemists onwards, but now in the 21st century we are beginningto understand how they can lead us to a new domain of self-organized structures of semipermeable membranesand amorphous as well as polycrystalline solids produced at the interface of chemistry, fluid dynamics, andmaterials science. We propose to call this emerging field chemobrionics.


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Dynamics of buoyancy-driven flows in the Earth’s subsurface and in the ocean

Silvana CardosoDept. of Chem. Eng. and Biotechnology, University of Cambridge, UK.

Chemical and physical disequilibrium in the ocean, atmosphere and in the Earth’s subsurface can lead togigantic convective flows of methane and carbon dioxide. Examples in the atmosphere and oceans include theturbulent plumes formed during the Icelandic volcanic eruption (2010), the BP oil spill in the Gulf of Mexico(2010), and the large number of methane plumes found recently in the Arctic Sea (2013). In the sub-surface,when carbon dioxide dissolves in the water contained in the porous rock, the heavy CO2-rich fluid sinksdriving vigorous laminar convection. A further example is the flow of dissolved methane under osmotic forcesin the porous rock near mud volcanoes on the seabed. In this talk, we focus on the non-linear interactionbetween hydrodynamics and chemistry, including chemical reaction or dissolution/precipitation, in such flows.Using complementary theoretical, numerical and experimental approaches, we quantify the spatiotemporaldevelopment of the flow pattern caused by ongoing chemical processes and mixing in the fluids.


Network physiology: How complex physiologic organ systems dynamically interact

Plamen Ch. IvanovPhysics Department, Boston University and Division of Sleep Medicine, Harvard Medical School, USA.

The human organism is an integrated network where multi-component organ systems, each with its ownregulatory mechanisms, continuously interact to optimize and coordinate their function. Organ-to-organinteractions occur at multiple levels and spatiotemporal time scales to produce distinct physiologic states: wakeand sleep; light and deep sleep; consciousness and unconsciousness. Disrupting organ communications canlead to dysfunction of individual systems or to collapse of the entire organism. Yet, we know almost nothingabout the nature of the interactions between diverse organ systems and their collective role in maintaininghealth. We propose a framework to probe dynamical interactions among physiological systems, and we identifya physiological network. We find that each physiological state is characterized by a specific network structure,demonstrating a robust interplay between network topology and physiologic function. Across physiologicalstates, the network undergoes topological transitions associated with fast reorganization of physiologicalinteractions on time scales of a few minutes, indicating high network flexibility in response to perturbations.The proposed system-wide integrative approach facilitates the development of a new field, Network Physiology.

9:00-9:45, Tuesday 8 September.

Rayleigh-Benard instability in curved elastic bilayer systems: Wrinkles, dimples,and the early universe

Norbert StoopDepartment of Mathematics, MIT, Cambdrige MA, USA.

Wrinkling in curved bilayer surfaces is a ubiquitous phenomenon, occuring, for instance, in embryogenesis,biological tissue differentiation or structure formation in heterogenous thin films. Due to the curved substrateand the strong nonlinearities in the elastic strains, predictions for the wrinkling morphology are notoriouslydifficult to obtain using classical analysis. Here, we choose a different approach and derive a generalizedSwift-Hohenberg theory to describe wrinkling morphologies and their pattern selection. Testing the theoryagainst experiments on spherically shaped surfaces, we find quantitative agreement with analytical predictionsfor the phase transition curves separating labyrinth, hybrid and hexagonal wrinkling phases. As our approachbuilds on general differential-geometric properties, it can be extended to arbitrary surfaces. To demonstratethe general approach, we apply our wrinkling theory to toroidal geometries in the hexagonal wrinkling phaseas a generic means to study defect formation.


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Chaos in optimal communication waveforms

Ned CorronU.S. Army Redstone Arsenal, AL, USA.

Modern communication technology is built upon the foundation established by Nyquist, Shannon, Wienerand others in the 1940s, whose theories enabled the rigorous derivation of optimal solutions to practicalcommunication problems. In this talk, we apply the methods of communication theory to derive optimalwaveforms for transmitting information through noise using very simple filters as receivers. Specifically wepresume passive, linear RLC filters and derive the communication waveforms that maximize the receiversignal-to-noise performance. From routine application of standard methods, we surprisingly find that theoptimal communication waveforms are provably chaotic. We extrapolate from simple examples to argue thatthe optimal communication waveform for any stable infinite impulse response filter is similarly chaotic. If true,this conjecture implies the phenomena of nonlinear dynamics and chaos are fundamental and essential to fullunderstanding of modern communication theory.


Hierarchical block matrices as looking glasses for multi scale biology

Pietro Lio’Dept. of Computer Science, University of Cambridge, UK.

In this talk I will discuss the utility of hierarchical block matrices for calibrating multi omics data and toanalyse multi scale biological systems from chromosome dynamics to tissue dynamics.


Correlations in the brain

Lucilla de ArcangelisSeconda Universita di Napoli, Italy.

Neuronal avalanches are a novel mode of spontaneous brain activity, experimentally found in vitro and invivo, which exhibits a robust critical behaviour. The temporal organization of neuronal avalanches can becharacterized by the distribution of waiting times between successive events. Experimental measurementsin the rat cortex in vitro exhibit a non-monotonic behavior, not usually found in other natural processes.Numerical simulations provide evidence that this behavior is a consequence of the alternation between states ofhigh and low activity, leading to a dynamic balance between excitation and inhibition. During these differentstates, both the single neuron behaviour and the network excitability level, keeping memory of past activity,are tuned by homeostatic mechanisms. This behavior has been verified on a larger scale, i.e., on fMRI datafrom resting patients. By monitoring temporal correlations in high amplitude BOLD signal, we find that theactivity variations with opposite sign are correlated over a temporal scale of few seconds, suggesting a criticalbalance between activity excitation and depression in the brain.

9:00-9:45, Wednesday 9 September.

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Conserved Ising model on the human connectome

Daniele MarinazzoGent University, Belgium.

A crucial issue interesting experimental and computational neuroscientists is the link between brain structureand function. A typical approach to address this problem consists in implementing a dynamical model on theknown structural architecture of the brain and observing the resulting emerging dynamics. Several families ofdynamical models have been used to this purpose, ranging from the most abstract ones to highly biologicallymotivated compartmental models. All these classes of models were somehow able to reproduce the typicalpatterns of functional connectivity (statistical dependencies between time series at the different brain locations)observed in real data, characterized by long-range correlations. The common characteristic of the modelsbehind this result is the metastability (or criticality, or balanced state): these correlations arise when thelinks are not too strong nor to weak, and the individual systems somehow excitable, but not too much. Acharacteristic which is rarely reproduced in these general models is the presence of negative correlations. Inthis study we hypothesize that these negative correlations are a direct consequence of a conservation law, andwe show this by implementing an Ising spin model with conserved magnetization (Kawasaki dynamics) on thebrain structural architecture. In this way we observe patterns of long range correlations, both positive andnegative, in networks with rough and fine spatial resolution.


Spatiotemporal dynamics of neuron activity in brain microcircuits

Egidio D’AngeloDip. Scienze del sistema nervoso, Universita di Pavia, Italy.

I will present a realistic computational model of the cerebellar granular layer to explain how it can transformincoming mossy fiber signals into new spike patterns to be related to Purkinje cells. This model is used toaddress four main functional hypotheses: center-surround organization, time-windowing, high-pass filtering inresponses to spike bursts and coherent oscillations in response to diffuse random activity. The model networkwas activated using patterns inspired by those recorded in vivo. Burst stimulation of a small mossy fiber bundleresulted in granule cell bursts delimited in time (time windowing) and space (center-surround) by networkinhibition. This burst-burst transmission showed marked frequency-dependence configuring a high-pass filterwith cut-off frequency around 100 Hz. The contrast between center and surround properties was regulated bythe excitatory-inhibitory balance. The stronger excitation made the center more responsive to 10-50 Hz inputfrequencies and enhanced the granule cell output (with spike occurring earlier and with higher frequency andnumber) compared to the surround. Finally, over a certain level of mossy fiber background activity, the circuitgenerated coherent oscillations in the theta-frequency band. All these processes were fine-tuned by NMDAand GABA-A receptor activation and neurotransmitter vesicle cycling in the cerebellar glomeruli. This modelshows that available knowledge on cellular mechanisms is sufficient to unify the main functional hypotheses onthe cerebellum granular layer and suggests that this network can behave as an adaptable spatio-temporal filtercoordinated by theta-frequency oscillations.


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Rolling and synchronization in dense packings of spheres

Hans HerrmannComputational Physics, ETH Zurich, Switzerland.

A large family of packing topologies allows for slip-less rotations between space-filling touching disks orspheres and thus form systems of bearings. I will discuss their construction and their fractal dimensions.Bearings are mechanical dissipative systems that, when perturbed, relax toward a synchronized (bearing) state.In fact bearings can be perceived as physical realizations of complex networks of oscillators with asymmetricallyweighted couplings. Accordingly, these networks can exhibit optimal synchronization properties tuning ofthe local interaction strength as a function of node degree. I show that, in analogy, the synchronizability ofbearings can be maximized by counterbalancing the number of contacts and the inertia of their constitutingrotor disks through a power-law mass-radius relation with an optimal exponent alpha. Under this condition,and regardless of the presence of a long-tailed distribution of disk radii composing the mechanical system, theaverage participation per disk is maximized and the energy dissipation rate is homogeneously distributed amongelementary rotors. The synchronization of rotations occurs in avalanches following a broad size distribution.The bearing configurations fulfill Kolmogoroff scaling and display Richardson’s diffusion law in the limit ofsmall Stokes numbers and constitute also an interesting toy model for turbulence. In two dimensions there existmany space-filling solutions of different topologies classified by three integers, while in three dimensions upto now we only know one topology, but which has a many bearing states classified by four real positive numbers.


Treating many-body quantum systems by means of classical mechanics

Andrey KolovskyL.V. Kirensky Institute of Physics, Siberian Branch of Russian Academy of Sciences, Russia.

Many-body physics of identical particles is commonly believed to be a sovereign territory of QuantumMechanics. The aim of this talk is to show that it is actually not the case and one gets useful insights into aquantum many-body system by using the theory of nonlinear dynamical systems. In the talk we focus on oneparadigmatic model of many-body quantum physics - the Bose-Hubbard model, which, in particular, describesinteracting ultracold Bose atoms in an optical lattice. After a preliminary, purely quantum analysis of thesystem we introduce a classical counterpart of the Bose-Hubbard model and its governing equations of motion.We analyze these equations for the problem of Bloch oscillations of cold atoms where a number of experimentalresults are available. We compare the results obtained by using pure classical arguments with those obtainedquantum-mechanically, and with those observed in the laboratory experiment.

9:00-9:45, Thursday 10 September.

Exploring topological and magnetic order with ultracold fermions in optical lattices

Gregor JotzuInstitute for Quantum Electronics, ETH Zurich, Switzerland.

Complex quantum many-body systems are ubiquitous in nature, yet their behaviour often remains verychallenging to predict with analytical or numerical calculations - especially when it comes to dynamics.However, using ultracold atoms in optical lattices it is possible to create precisely tunable, yet very accessiblecomplex systems, which can be probed with a variety of observables. Using this experimental set-up, wedemonstrate how a periodically modulated system can be described by an effective Floquet-Hamiltonian onlonger time-scales - even when driving the system far from equilibrium. This allows for implementing Haldane’smodel for a topological insulator by applying an oscillating force to a honeycomb lattice. A transverse driftarising from a non-zero Berry curvature, as well as a closing band-gap at the transition between two topologicalregimes, are observed. Furthermore we present the dynamics of anti-ferromagnetic correlations in the Hubbardmodel. Starting from a situation where short-range correlations are present, we deform the lattice geometry,on time-scales ranging from the sudden to the adiabatic regime. We then study how correlations re-arrange asa function of time.


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Explosive synchronization of networked oscillators

Stefano BoccalettiISC CNR Firenze, Italy.

Recently, it was pointed out that, for an ensemble of networked phase oscillators, the transition fromincoherence to synchronization can be first-order like, discontinuous and irreversible, called explosive syn-chronization (ES). Since its finding in 2005, ES has been paid a great attention, as abrupt transitions inreal world networks include epileptic seizures in the brain, cascading failure of power grids and jamming inthe Internet. For instance, ES was studied in the context of periodic phase oscillators for scale-free (SF)networks, with an ad-hoc imposed positive correlation between the natural frequencies of the oscillators andthe degrees of the nodes, and the experimental verification was given with electronic circuits. Later on,ES was described for generic network’s topologies (either SF or non-SF) in a modified Kuramoto model,with a positive correlation between the natural frequencies of oscillators and their coupling strengths. Theaccepted state of knowledge on this matter is that ES has a basic microscopic root in the frustration of thepath leading the system to synchronize. I my talk, I will discuss all different methods to induce ES in ageneric network, and highlight the microscopic mechanisms that are at the basis of its emergence and generality.


Nonlinear systems characterization using phase space density

Thomas L. CarrollUS Naval Res. Labs, Washington DC, USA.

In the early days of nonlinear dynamics, density base measures such as fractal and multifractal dimensionswere used to characterize attractors from nonlinear systems. While measures based on derivatives havebecome more popular recently, density is still a useful way to characterize attractors. In this work, a simpleexperiment consisting of a pair of operational amplifiers is driven with a chaotically modulated signal. Theoutput signal is embedded in phase space and characterized by its density. Although op amps are usuallyconsidered to be linear devices, comparing densities as the op amp gain increases reveals the nonlineargain of the amplifier. Clustering analysis shows that amplifiers tend to cluster by gain level, not by theindividual amplifier, suggesting that the nonlinearities in different amplifiers are similar. It is also notedfor system characterization that a chaotically modulated signal works better than a randomly modulated signal.


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Monday 7 September 16:10-17:50

Room 1: Control

Stabilization of hyperbolic Plykin attrac-tor by the Pyragas method

Sergey Belyakina, Arsen Dzhanoeva and SergeyKuznetsovb

In the present contribution consideration is beinggiven to an autonomous physical system which ischaracterized by the presence of the attractor of ahyperbolic type. We study the possibility of control-ling and stabilizing the Plykin attractor of this typeby the Pyragas method. The choice of the method ofcontrol. As such it is possible to use an external signalor the introduction of additional delayed feedback.(Both methods can be realized primarily during theschematic simulation then in a real experiment). Itmight also be interesting to think about the realizationof a more complicated scheme of control of the typesuggested in the work for the stabilization of unstableperiodic orbits belonging to the attractor.

aPhysics of Faculty, State University of Moscow, Moscow119991(2), Russia; bFaculty of Nonlinear Processes, Depart-ment of Dynamic Systems, State University of Saratov, Saratov410012, [email protected]

Method of generalized synchronizationdetection without using an auxiliary sys-tem approach

Vladimir Ponomarenkoa and Mikhail Prokhorova

Designing and development of methods for detect-ing generalized synchronization is an actual problem ofmodern nonlinear dynamics [1-2]. The criterion for es-tablishing the generalized synchronization is the pres-ence of a functional relationship between the states ofunidirectionally coupled dynamical systems [1]. Differ-ent methods have been proposed to detect the regime ofgeneralized synchronization. The most popular amongthem are the auxiliary system approach [3], the con-ditional Lyapunov exponent calculation [4], and thenearest neighbor method [5].

The most suitable method for detecting the gener-alized synchronization in a physical experiment is themethod of the auxiliary system. However, its majordrawback is the necessity to implement two identicalgenerators, the response system and auxiliary system.In this paper, we propose a new method of general-ized synchronization which exploits the idea of auxil-iary system approach, but utilizes only one responsesystem which is driven in turn by the transmitted sig-nal itself and its delayed copy. If we drive the self-oscillating response system twice with the same input

signal from the autonomous drive system, then afterthe transient process it will exhibit identical oscilla-tions in both cases in the presence of the generalizedsynchronization between the drive and response sys-tems.

In this paper, the efficiency of the proposed methodis demonstrated in a numerical experiment for unidi-rectionally coupled time-delay systems. At first, withinthe time interval τ we drive the response system in thereceiver with the signal of the drive system. Then,within the same time interval τ we drive the same re-sponse system with the delayed signal incoming fromthe output of the delay line having the delay time τ .At last, we compare the signals of the response sys-tem in the considered two cases. With this purposewe calculate the difference between the signal at theresponse system output and the signal of the responsesystem which is passed through one more delay linewith the delay time τ . In the presence of the general-ized synchronization, this difference vanishes after thetransient process.

It is shown that the proposed method allows oneto detect the presence of generalized synchronizationeven in the presence of very high levels of noise compa-rable to the amplitude of the drive signal. The methodis promising for constructing a secure communicationsystem with high tolerance to noise in a communicationchannel.

[1] N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, H.D.I. Abar-banel “Generalized synchronization of chaos in directionallycoupled chaotic systems,” Phys. Rev. E, vol. 51, pp. 980-994, 1995.

[2] L. M. Pecora, T. L. Carroll, “Synchronization in chaotic sys-tems,” Phys. Rev. Lett., vol.64, pp.821–824, 1990.

[3] H. D. I. Abarbanel, N. F. Rulkov, M. M. Sushchik, “Gen-eralized synchronization of chaos: The auxiliary system ap-proach,” Phys. Rev. E, vol.53, pp.4528–4535, 1996.

[4] L. M. Pecora, T. L. Carroll, J. F. Heagy “Statistics formathematical properties of maps between time series em-beddings,” Phys. Rev. E, vol. 52, pp.3420-3439, 1995.

[5] K. Pyragas, “Conditional Lyapunov exponents from time se-ries,” Phys. Rev. E, vol.56, pp. 5183–5188, 1997.

aSaratov Branch of the Institute of Radio Engineering and Elec-tronics of Russian Academy of Sciences, 38 Zelyonaya Street,Saratov 410019, [email protected], [email protected]

Non-identical chaos anti-synchronizationvia passive control

Ugur Erkin Kocamaza, Yılmaz Uyaroglub, MustafaUrinc and Tugrul Tascıd

This paper investigates the anti-synchronizationof non-identical chaotic systems by means of passivecontrol technique. Based on the property of passivitytheory, the passive controllers are constructed for theanti-synchronization between Lorenz and Liu chaoticsystems. Lyapunov function is used to realize thatthe passive controllers ensure the global asymptoticstability of error system. Numerical simulationsare performed to demonstrate the efficiency of theproposed non-identical anti-synchronization strategy.

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aDepartment of Computer Technologies, Vocational School ofKaracabey, Uludag University, 16700 Karacabey, Bursa, Turkey;bDepartment of Electrical & Electronics Engineering, Facultyof Engineering, Sakarya University, 54187 Serdivan, Sakarya,Turkey; cDepartment of Information Systems Engineering, Fac-ulty of Computer and Information, Sakarya University, 54187Serdivan, Sakarya, Turkey; dDepartment of Computer Engineer-ing, Faculty of Computer and Information, Sakarya University,54187 Serdivan, Sakarya, [email protected], murin, [email protected]

Controlling chaotic permanent magnetsynchronous motor with a single statespeed feedback controller

Ugur Erkin Kocamaza and Yılmaz Uyaroglub

This study investigates the control of chaoticpermanent magnet synchronous motor with a singlestate speed feedback controller. Time series andphase por-traits of chaotic permanent magnet syn-chronous motor are presented graphically from itsdifferential equations. The sufficient conditions forthe speed feedback control gains are obtained bythe Routh-Hurwitz criterions. Numerical simulationsare demonstrated to validate the feasibility of theproposed method. Simulation results have also shownthat the controlled permanent magnet synchronousmotor system effectively stabilizes towards its non-zeroequilibrium points in the state space.

aDepartment of Computer Technologies, Vocational School ofKaracabey, Uludag University, 16700 Karacabey, Bursa, Turkey;bDepartment of Electrical & Electronics Engineering, Facultyof Engineering, Sakarya University, 54187 Serdivan, Sakarya,[email protected], [email protected]

Monday 7 September 16:10-17:50

Room 2: Synchronization

Chaos synchronization between financeand Rikitake systems by active controlwith unknown parameters

Ugur Erkin Kocamaza, Gultekin Cagılb, YılmazUyarogluc and Zeynep Cagılb

The aim of this research is to investigate the non-identical synchronization of a chaotic finance system.Once the chaotic finance system is synchronized to thewidely-used Rikitake chaotic system, all the theoriesand applications based on the Rikitake chaotic systemsuch as control can be applied for the finance system.Active controllers are designed for the synchronizationof chaotic finance system to Rikitake chaotic systemwith unknown parameters. The asymptotical stabilityof synchronization errors is ensured based on the

properties of Lyapunov theory. Numerical simula-tions are demonstrated to validate the theoreticalanalyses. They have also shown that these chaoticsystems can be synchronized in a proper amount oftime with the active controllers, which verifies theefficiency of proposed chaos synchronization technique.

aDepartment of Computer Technologies, Vocational Schoolof Karacabey, Uludag University, 16700 Karacabey, Bursa,Turkey; bDepartment of Industrial Engineering, Faculty ofEngineering, Sakarya University, 54187 Serdivan, Sakarya,Turkey; cDepartment of Electrical & Electronics Engineering,Faculty of Engineering, Sakarya University, 54187 Serdivan,Sakarya, [email protected], cagil, uyaroglu,[email protected]

Synchronization of chaotic three timescales brushless DC motor system bymeans of one state passive controller

Yılmaz Uyaroglua, Ugur Erkin Kocamazb and BarısCevhera

This study investigates the synchronization of twoidentical chaotic three time scales Brushless DC Motor(BLDCM) systems with the passive control method.The three time scales BLDCM system is describedbriefly from its differential equations, time series andphase space portraits are given graphically. Based onpassive control theory, a Lyapunov function is usedto ensure the asymptotic stability of error system.Numerical simulations are presented to validate thefeasibility of the proposed method. The simulationresults are satisfied in view of achieving the synchro-nization of all states using only one state controller.

aDepartment of Electrical & Electronics Engineering, Facultyof Engineering, Sakarya University, 54187 Serdivan, Sakarya,Turkey; bDepartment of Computer Technologies, VocationalSchool of Karacabey, Uludag University, 16700 Karacabey,Bursa, [email protected],[email protected]@sakarya.edu.tr

Chaotic quaternionic multidirectionalassociative memory with adaptive scal-ing factor of refractoriness

Ryohei Itoa and Yuko Osanaa

The association ability of associative memories com-posed of chaotic neuron models or chaotic neuron-based models such as chaotic complex-valued neuronmodel and chaotic quaternionic neuron model are verysensitive to chaotic neuron parameters such as scalingfactor of refractoriness α, damping factor k and so on.And, in these models, appropriate parameters have todetermined by trial and error. In this research, wepropose a Chaotic Quaternionic Multidirectional As-sociative Memory with adaptive scaling factor of re-fractoriness which can realize one-to-many associations

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of multi-valued patterns and whose parameters can bedetermined automatically.

The proposed Chaotic Quaternionic MultidirectionalAssociative Memory with adaptive scaling factor ofrefractoriness has three or more layers as similaras the conventional Chaotic Quaternionic Multidirec-tional Associative Memory [1]. Each layer consists oftwo parts; (1) Key Input Part composed of quater-nionic neuron models [2] and (2) Context Part com-posed of chaotic quaternionic neuron models [3]. Sincechaotic quaternionic neuron models in the ContextPart change their states by chaos, plural multi-valuedpatterns corresponding to the input common term canbe recalled, that is, one-to-many association can berealized. In the conventional Chaotic QuaternionicMultidirectional Associative Memory, scaling factor ofrefractoriness α is tuned manually. In the proposedmodel, scaling factor of refractoriness α varies depend-ing on time and average internal states of neurons.

Fig. 1: One-to-Many Association Ability.

We compared the one-to-many association ability inthe 3∼6-layered proposed model with the well-turned3∼6-layered conventional Chaotic Quaternionic Multi-directional Associative Memory with variable scalingfactor of refractoriness (Conventional Model). Figure1 shows the one-to-many association ability of the pro-posed model and the conventional model. As shownin this figure, the one-to-many association ability ofthe proposed model almost equals to that of the con-ventional model. We also examined the one-to-manyassociation ability of the various size proposed modeland confirmed that the proposed model in various sizehas good one-to-many association ability as similar asin the result shown in Fig. 1.

[1] T. Okutsu and Y. Osana: “Chaotic quaternionic multi-directional associative memory”, Proceedings of Interna-tional Symposium on Nonlinear Theory and its Applications,Luzern, 2014.

[2] T. Isokawa, H. Nishimura, N. Kamiura and N. Matsui: “Fun-damental properties of quaternionic Hopfield neural net-work”, International Journal of Neural Systems, Vol. 18,No. 2, pp. 135-145, 2008.

[3] Y. Osana: “Chaotic quaternionic associative memory”, Pro-ceedings of IEEE and INNS International Joint Conferenceon Neural Networks, Brisbane, 2012.

aSchool of Computer Science, Tokyo University of Technology,Tokyo, [email protected]

Explosive synchronization in complexnetwork

Xiyun Zhanga

Recently, discontinuous synchronization transitioncalled explosive synchronization has become a hottopic. In my poster, I will introduce our work on explo-sive synchronization, including 3 parts: 1) A weightedmodel which can generate explosive synchronization incomplex network with different degree distribution anddifferent frequency distribution of nodes, 2) The sup-pressive rule in explosive synchronization. Meanwhile,on microscope, explosive synchronization can be re-garded as explosive percolation in dynamical space, 3)Explosive synchronization in adaptive and multilayernetworks. In this part, a model with no correlationbetween frequency and coupling strength is introduced.

aUniversity of Potsdam, Institut fur Physik und Astronomie,Potsdam, Germany.zxy [email protected]

Tuesday 8 September 11:10-12:25

Room 1: Networks and Applications

Mechanisms of complex pattern forma-tion in chemical systems

Andrey A. Polezhaeva

Spatial-temporal self-organization has long beenthe subject of both experimental and theoreticalinvestigations. So far, not only autowaves and dissi-pative structures are discovered but such new typesof patterns as antispirals, wave packets, segmentedwaves, oscillons - localized oscillating spots and others.All this variety of patterns were observed in partic-ular in Belousov-Zhabotinsky reaction proceeding inmicroemulsion (BZ-AOT system). Mechanisms offormation of some of these patterns are quite clearbut others need explanation. Now it is commonknowledge that diffusion can cause instability of theuniform state in a spatially distributed system. It wasfirst demonstrated by Turing in his classical paper,published in 1952. Turing instability is the reasonfor formation of non-uniform stationary patterns(“dissipative structures”) which can be obtainedin relatively simple two component models of the“reaction-diffusion” type. In the present talk I willshow that other experimentally observed patternsneed for their explanation more complex modelscontaining at least three or even four equations. The

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reason is that in these patterns either wave instabilityis involved, which needs at least a three-variablemodel, or they are the consequence of interaction ofseveral instabilities, each of which being described bya corresponding sub-model. It will be demonstratedthat some complex patterns, such as segmental wavesand oscillons, for instance, can be explained in theframe of four-component reaction-diffusion modelsconsisting of two interacting two-variable sub-models.

aP.N. Lebedev Physical Institute of the Russian Academy ofSciences, Leninskiy prospekt, 53, 119991, Moscow, [email protected]

Hebbian learning clustering using net-works of Rulkov neurons

Jenny Helda and Ruedi Stoopa

The ability to group data items into clusters basedon similarity is essential for the analysis of the struc-ture of a system. Despite decades of development,clustering of big data sets and real-time clusteringremain a challenge. Biology-inspired approaches usinglocal learning among neurons, such as the Integrate-and-Fire Hebbian Learning Clustering (HLC), havebeen shown to be well suited for tackling intrinsicclustering problems, but in past implementationsrequired large computation times. Here, we proposea clustering algorithm that is based on pair-wiseinteractions in a network of Rulkov neurons. Hebbianlearning is used to favour the potentiation of intra-cluster synaptic connections and the depression ofextra-cluster connections, so that clusters emerge asgroups of strongly coupled, synchronised neurons. Thediscrete time Rulkov neuron dynamics overcome timecomplexity limitations of former (time continuous)implementations. The algorithm is able to find anatural, system-dependent number of clusters ofarbitrary shape in an unsupervised way, even in thepresence of background noise data. We present severaldata sets and compare the clustering results to thoseof standard algorithms. We outperform traditionalalgorithms such as k-means and Ward’s clustering byfar in terms of quality. We also produce clusteringresults of at least equal and often higher quality thanprevious HLC implementations, with computationtimes reduced by two orders of magnitude.

aInstitute of Neuroinformatics and Institute of ComputationalScience, University of Zurich and ETH Zurich, [email protected]

Saturation effect produces deviationsfrom power law statistics in real-worldnetworks

Tom Lorimera, Florian Gomeza and Ruedi Stoopa

The distribution of node degree in complex real-world networks has often been claimed to follow apower law, the origin of which is generally attributed tothe fundamental principle of preferential attachment.In all real-world networks however, a perfect powerlaw is not observed, and is instead often terminatedby a hump at high node degree. Imperfections of thissort have previously been explained away as finite sizeeffects by reference to the thermodynamic limit. Weshow, however, that such humps arise as the result ofa second fundamental principle active during networkgrowth: saturation. We introduce a simple networkgrowth algorithm which exemplifies these two funda-mental principles, and reproduces the observed powerlaw deviations. Through a semi-analytic treatment, wedemonstrate that the origin of the hump may be under-stood in terms of a mean-field ‘failure function’ whichexpresses the edge-saturation of the nodes in the net-work. Numerical investigation of this function revealsremarkable scaling properties, and it is approximatedas a double power law function of network size. Apply-ing this approximation in a conventional node degreerate equation reproduces the growth behaviour of thealgorithm, and demonstrates the link between satura-tion and the formation of the hump. We calculate aphase diagram of the hump size and power law expo-nent as a function of our algorithm parameters, whichsuggests a new window into the understanding of meso-scale network structures and processes from modellingthe power law deviations of network statistics.



Room 2: Stochastic Systems

Bayesian parameter inference forstochastic differential equation mod-els

Carlo Alberta

Bayesian parameter inference for stochastic differen-tial equation models is a computationally hard prob-lem as the density of the posterior parameter distri-bution is given by a path-integral. We rephrase thisBayesian inference problem as the problem of simu-lating the dynamics of a linear polymer with harmonicbonds in an external potential, and with model param-eters representing degrees of freedom that couple to allother system coordinates. Depending on the numberof measurement points and the number of discretiza-tion points the dynamics of the system happens onvery different time-scales. Using a suitable parameter-ization the fastest dynamics reduces to the dynamics

11

of uncoupled standard harmonic oscillators and can bedisentangled from the slower dynamics by means of aTrotter formula. The resulting algorithm is highly par-allelizable, very fast, and, employing automated differ-entiation techniques, readily applicable to a wide rangeof inference problems.

aEawag, Swiss Federal Institute of Aquatic Science and Technol-ogy, 8600 Dubendorf, [email protected]

Conditions for persistence of stochasticprocesses

Raffaello Seria

Consider a K−dimensional stochastic processXtt∈Z describing a physical, chemical or biologicalsystem with nonnegative components such that 0 isan absorbing state for each component. Leading ex-amples concern ecosystems, with each component de-scribing the abundance of a species, or chemical sys-tems, in which each component describes the amountof a reagent. In the ecosystem example, reaching thevalue 0 corresponds to extinction of the species. Theabsorption condition, i.e. the fact that when a com-ponent reaches the value 0 it will take on that valuethereafter, means that no recovery is possible from ex-tinction. We suppose that the stochastic process canbe described by an Iterated Function System (IFS);this is equivalent to the requirement that the stochas-tic process is first-order Markovian. We then describe acondition, called “stochastic boundedness,” first intro-duced by P.L. Chesson, that guarantees that no com-ponent of the system is absorbed by 0. We provide asufficient condition for stochastic boundedness involv-ing the functions describing the IFS. As this sufficientcondition is quite difficult to check, we provide a sta-tistical procedure based on sampling from the IFS totest for it.

aDepartment of Economics, Universita degli Studi dell’Insubria,Como, [email protected]

Detecting influences - a network analysisof the European bond market based onpartial mutual information

Martin Schuelea, Stefan Gluegea, Peter Schwendnerb

and Thomas Otta

The need for an analysis of supposed dependenciesbetween variables or processes arises in many areasof scientific investigation. Typically, the correlationstructure of the differenced time series generated bythe underlying processes is studied, i.e., the structurearrived at by computing pair-wisely the Pearson corre-lation coefficients. Often, one is particularly interestedin temporal changes of this correlation structure which

may point to structural breaks. As the correlation co-efficient is a symmetric measure, such an analysis doeshowever not reveal the influences that bring out thesecorrelations, i.e., whether a correlation is due to somedirect influence between variables or rather due to theinfluence of some other variable. One way to deal withthis issue is to consider the partial correlation coeff-cient which allows to separate different possible influ-ences. Based on the partial correlation measure, onemay then derive some measure of influence that allowsto set up and analyse a network depicting the directedinfluences between variables, see e.g. Schwendner etal. [1]. This approach raises however the following dif-ficulties: First, the Pearson correlation coeffcient onlydetects a possible linear dependence between variablesand, second, in order to avoid spurious correlations, thedifferenced time series data is assumed to be stationary.In response to this, we propose in this contribution todetect influences of variables by using an influence mea-sure based on the mutual information and the partialmutual information measure [2]. The mutual informa-tion measure can also detect nonlinear statistical de-pendencies between processes and, while the involvedstochastic processes are usually assumed to be station-ary, information theory may provide ways to deal alsowith the nonstationary case. Partial mutual informa-tion is then postulated in analogy to partial correlationand allows to separate different indirect and direct in-fluences of variables. Based on partial mutual infor-mation, we further postulate a measure of influencethat allows to set up a network of directed influences,generalized to the nonlinear and possibly nonstation-ary case. We illustrate this fairly general method byapplying it to financial market data, namely the move-ments of European government bond yields in the pe-riod 1990-2015. An analysis of the correlation and in-fluence structure of the data has been carried out in[1], which further allows to compare and discuss bene-fits and pitfalls of the two approaches.

[1] P. Schwendner, M. Schuele, T. Ott and M. Hillebrand, “Eu-ropean Government Bond Dynamics and Stability Policies:Taming Contagion Risks”, Available at SSRN 2015.

[2] S. Frenzel and B. Pompe, “Partial Mutual Information forCoupling Analysis of Multivariate Time Series”. PhysicalReview Letters, 99, 204101, 2007.

aInstitute for Applied Simulation, Zurich University of Ap-plied Sciences, Switzerland; bCenter for Alternative Investments,Zurich University of Applied Sciences, Switzerland.martin.schuele, stefan.gluege, peter.schwedner, [email protected]



12

Analysis of digital maps based on simplefeature quantities

Hiroyuki Kusanoa, Hiroki Yamaokaa and ToshimichiSaitoa

The digital map (Dmap) is digital dynamical systemdefined on a set of lattice point [1]. Since the numberof the lattice point is finite, the steady state is a pe-riodic orbit (PEO). Although analog one-dimensionalmaps (e.g., the logistic map) can generate chaos, theDmap can generate various PEOs. The Dmaps are re-lated to various systems such as cellular automata, dig-ital spiking neurons, dynamic binary neural networks,and logical/sequential circuits ([1], [2], and referencestherein). Such digital systems have been applied tovarious engineering systems. Analysis of the Dmapsis important not only as a basic study but also forengineering applications. The Dmap is described byθn+1 = FD(θn), θn ∈ LN ≡ l1, l2, ..., lN, where LN isa set of N lattice points l1 to lN . Figure 1 illustratesthe Dmap where several PEOs co-exist. Depending oninitial condition and parameters, the Dmap exhibits ei-ther PEO. In general, the Dmap can have a variety ofPEOs and transient phenomena. In order to analyzeof Dmap, we introduce two feature quantities. Thefirst quantity α represents plentifulness of the steadystates. The second quantity β represents deviation oftransient phenomena to steady states. One Dmap cor-responds to one point on the α vs β plane on which wecan classify/consider the dynamics. There exist manyexamples of the Dmaps and their general considerationis extremely hard. For simplicity, we consider one ex-ample: the digital tent map given by discretizing thetent map on the set of lattice points. Using the featurequantities, we have given basic classifications.

Fig. 1: Digital tent map. Left to right: Fixed points; PEO

with period 2; PEO with period 4.

[1] H. Yamaoka, N. Horimoto, and T. Saito, Proc. ICANN(2014) 73.

[2] M. Schule and R. Stoop, Chaos 22, 043143 (2012).

aHosei University, Tokyo, [email protected]

New tools to determine the optimal em-bedding of a time series

Leonardo Riccia, Davide Tabarellia and MatteoFranchia

According to the Takens-Mane embedding theorem,embedding makes up a basic tool to analyze a time

series and thus investigate the dynamical propertiesof the underlying chaotic system. Unfortunately theembedding theorem provides no clues on how to choosethe embedding dimension m and the embedding lagL. Although in the last two decades several methodshave been devised to tackle this crucial issue, aconclusive criterion to make the most appropriatechoice is still lacking. We present a new approach thatrelies on the analysis of the statistical properties ofthe uncertainty of the maximum Lyapunov exponent(MLE), calculated via the divergence rate method onfinite-time sequences [1]. Using chaotic systems withexplicit analytic representation that are widely usedas references in the scientific literature we show that‘good’ embedding pairs (m,L) tend to form Gaussian-like clusterings of the uncertainty. This property canbe used also in the reverse way: embedding pairsthat form quasi-normally distributed clusterings ofthe MLE uncertainty are to correspond to optimalembedding choices. The method complies with thetheory of the statistical properties of the finite-timeMLE first discussed by Grassberger, Badii and Politi[2]. A second aspect regards the investigation ofhow the MLE uncertainty scales with the samplingfrequency: the theory [2] predicts a power law scalingwith typical exponents (for example, -0.5 in thecase of continuous systems with short correlationtimes). We discuss how this scaling can be exploitedto provide an additional tool to identify optimalembedding parameters, and in particular the lag L.Finally, we present preliminary results concerningthe application of these methods to the analy-sis of time series generated by synthetic chaotic andnoisy systems and to electroencephalografic recordings.

[1] M. Franchi and L. Ricci, ”Statistical properties of the maxi-mum Lyapunov exponent calculated via the divergence ratemethod”, Phys. Rev. E 90, 062920 (2014).

[2] P. Grassberger, R. Badii, and A. Politi, ”Scaling laws forinvariant measures on hyperbolic and nonhyperbolic atrac-tors”, J. Stat. Phys. 51, 135 (1988).

[3] A. Prasad and R. Ramaswamy, ”Characteristic distributionsof finite-time Lyapunov exponents”, Phys. Rev. E 60, 2761(1999).

aDepartment of Physics and CIMeC, University of Trento,Trento, [email protected]

Hyperchaos and synchronization in par-alleled power converters

Yasuo Murataa and Toshimichi Saitoa

The paralleled systems of switching power convertershave been studied from fundamental and applicationviewpoints. In the fundamental study, the paralleledsystems are interesting examples of switched dynami-cal systems that can exhibit a variety of nonlinear phe-nomena [1,2]. In the applications, the paralleled sys-tems can realize current sharing and ripple reductionwhich are effective in robust and reliable power man-agement [2,3]. In these studies, analysis of nonlinear

13

phenomena is important and single power convertershave been studied sufficiently [2]. However, the anal-ysis of the paralleled systems is not easy because theyare higher dimensional systems with various complexbehavior. This paper studies hyperchaos and relatedbifurcation phenomena in the paralleled boost convert-ers (PBC). Figure 1 (a) shows a circuit model of thePBC. In the circuit, the input current iin is shared bythe two boost converters and the input current sharingis basic for efficient power extraction. Each converterincludes the switch Si and the diode Di (i = 1, 2) whichcan be either State A (Si conducting and Di blocking,xi rises) or State B (Si blocking and Di conducting, xidecays). We assume that the output voltage regulationis achieved and the output load is replaced with con-stant voltage sources Vo1 and Vo2. Applying a current-mode switching rule, the dynamics is described by thefollowing equation

dx1dt

=

−γx1 + a for State A

−γx1 − b1 for State B,

SW rule

State A→ State B if x1 > x2 at t = nT

State B→ State A if x1 = X−,

dx2dt

=

−γx2 + a for State A

−γx2 − b2 for State B,

SW rule

State A→ State B if x2 > x1 at t = nT

State B→ State A if x2 = X−,

where xi is proportional to ii (i = 1, 2) and X− is thelower threshold. The PBC has clock signal with periodT . The dimensionless parameters γ, a, b1, and b2 areproportional to 1/L, Vin, Vo1, and Vo2, respectively.Since this system is piecewise linear, the dynamics canbe analyzed precisely. Figure 1 (b) shows inverse-phasesynchronization that is suitable for current sharing andripple reduction. Figure 1 (c) shows hyperchaos wherethe orbit is expanding in two directions (x1 and x2). Asparameters vary, the PBC exhibit complicated bifur-cation phenomena between the inverse-phase synchro-nization and hyperchaos. The bifurcation phenomenaare investigated on b1 versus b2 plane. Presenting asimple test circuit, typical phenomena are confirmedexperimentally.

Fig. 1: Paralleled Boost Converters. (a) Circuit model. (b)

Inverse-phase synchronization for b1 = b2 = 0.5, γ = 1 = 0.3,

and X− = 0.05. (c) Hyperchaos for b1 = b2 = 0.05,

γ = a = 0.3, and X− = 0.05.

[1] P. Deivasundari, G. Uma and C. Vincent, IET Power Elec-tron., 7, (2014) 1235.

[2] T. Saito, T. Kabe, Y. Ishikawa, Y. Matsuoka, and H. Torikai,IJBC, 17, (2007) 3373.

[3] T. Ohata and T. Saito, Proc. IEEE/IECON (2013) 8389.

aHosei University, Tokyo, 184-8584 [email protected]

Simulating neural oscillations with map-based neurons

Karlis Kandersa and Ruedi Stoopa

Oscillations are a salient phenomenon in the nervoussystem spanning a large range of scale from single toni-cally spiking cells to ensembles of thousands of synchro-nized neurons. In order to simulate oscillatory behavioron the network scale relevant to the brain, one needsbiologically plausible neuron models and the computa-tional power to simulate networks with a large numberof such neurons. To satisfy both requirements, a solu-tion has been proposed in the form of low-dimensional,discrete map-based phenomenological neuron modelsthat are capable of a rich repertoire of neural responseswhile being computationally very inexpensive [1]. Anotable example is the Rulkov’s two-dimensional map[2] which can exhibit spike rate adaptation, chaoticspiking and bursting, and which can be tuned to havesimilar responses to the more complex, conductance-based Hodgkin-Huxley type models [3]. The collectivebehavior (e.g., synchronization) of a network is highlysensitive to the phase response properties of the singleneurons [4]. In the present study we analyze and ex-plain the phase responses to perturbations of spikingRulkov neurons and compare them to real neurons. Weshow that the models proposed in [2,3] can be classifiedas type I and type II neurons in terms of the bifurca-tion to the spiking state and, consequently, the typeof phase response curve. We characterize the depen-dencies of the phase response curves to perturbationstrength and spiking frequency, and conclude that theRulkov’s map can successfully replicate the phase re-sponse properties of biological neurons.

[1] Girardi-Schappo, M., Tragtenberg, M. H. R., & Kinouchi, O.(2013). A brief history of excitable map-based neurons andneural networks. Journal of Neuroscience Methods, 220(2),116–30.

[2] Rulkov, N. (2002). Modeling of spiking-bursting neuralbehavior using two-dimensional map. Physical Review E,65(4), 041922.

[3] Rulkov, N. F., Timofeev, I., & Bazhenov, M. (2004). Os-cillations in large-scale cortical networks: map-based model.Journal of Computational Neuroscience, 17(2), 203–23.

[4] Hansel, D., Mato, G., & Meunier, C. (1995). Synchronyin Excitatory Neural Networks. Neural Computation, 7(2),307–337.



Room 2: Coupled Oscillators

14

Complex bifurcations of Arnol’d tonguesgenerated in three-coupled delayed logis-tic maps

Daiki Ogusua, Shuya Hidakaa, Naohiko Inabab, Mune-hisa Sekikawac and Tetsuro Endoa

This study investigates quasi-periodic bifurcationsand Arnol’d resonance webs generated in three-coupleddelayed logistic maps. Complex bifurcation structureis observed when a conventional Arnol’d tonguetransits to a higher-dimensional Arnol’d tongue. Wediscovered that at least two periodic attractors coexistin the conventional Arnol’d tongue.

aDepartment of Electronics and Bioinformatics, Meiji Univer-sity, 214-8571 Kawasaki, Japan; bOrganization for the StrategicCoordination of Research and Intellectual Property, Meiji Uni-versity, 214-8571 Kawasaki, Japan; cDepartment of Mechanicaland Intelligent Engineering, Utsunomiya University, 321-8585Utsunomiya, [email protected], [email protected]

Chimera states in ensembles of time-delayed feedback oscillators with themean field

Danil Kulminskiya, Vladimir Ponomarenkoa andMikhail Prokhorova

Recently, investigation of specific states in ensemblesof coupled identical oscillators, named as chimerastates, attracts a lot of attention [1-3]. These statesare characterized by the presence of two differentclusters, in one of which the oscillators exhibit syn-chronous behavior, and in another, the asynchronousone. The chimera state can occur in ensemblesof bistable oscillators where depending on initialconditions each element of the ensemble can exhibitdifferent oscillating behavior. In the present paper weinvestigate the chimera state in a ring of time-delayedfeedback oscillators with a specific form of nonlinearfunction which are coupled through a mean field. Themean field is formed by summation of outputs of alloscillators. The obtained sum is filtered and fed intoeach oscillator as an external driving. The dynamicsof each oscillator in the ensemble is described bythe following equation: ε = −x + f(x(t − τ) + kγ),where τ is the delay time, ε is the parameter thatcharacterizes the inertial properties of the system, γis the mean field, k is the coupling strength, and f isa nonlinear function. All oscillators in the ensembleare identical. The nonlinear function has the followingform:f(x) = a sin(x − b), where a = 3 and b = −0.8.In this case, the time-delay system (1) possessesbistability. At the negative initial conditions thechaotic attractor is realized, while at the positiveinitial conditions the periodic attractor is realized. Weinvestigate the ensemble of six time-delayed feedbackoscillators coupled in a ring. Each oscillator consistsof a delay line with τ = 100, a nonlinear element, and

a low-pass first-order Butterworth filter with cutofffrequency fc = 1/ε = 0.4 . To form the mean fieldthe signals from the filter output of each oscillatorare added to a summator. Then the signal from thesummator output is passed through a low-pass filterand fed into each oscillator. The initial conditionsare chosen in such a way that the oscillators 1-3generate a chaotic attractor on the third harmonicof the basic mode, and the oscillators 4-6 generatea periodic attractor on the basic mode. Thus, twoclusters are formed in the ensemble. The structure ofthe considered ensemble corresponds to the Kuramotosystem of phase oscillators coupled through the meanfield [4] which shows the transition from synchronousto asynchronous dynamics under the change of thephase shift of the mean field. If the phase shift is lessthan π/2, then the ensemble exhibits synchronousbehavior, and if the phase shift is greater than π/2,then the ensemble exhibits asynchronous behavior. Wehave shown that under the change of the phase shift ofthe mean field the studied ensemble can exhibit threesubstantially different regimes. At the small phaseshift the oscillators 4-6 are synchronized (they forma cluster with periodic behavior), and the oscillators1-3 are phase synchronized. When the phase shiftis greater than π/2 for the third harmonic but lessthan π/2 for the basic mode, the oscillators 4-6 aresynchronized and the oscillators 1-3 are asynchronous.Under the greater phase shift, all oscillators in theensemble exhibit asynchronous behavior. Thus, wehave demonstrated the presence of the chimera statein the ensemble of time-delayed feedback oscillatorswith the mean field.

[1] D.M. Abrams, S.H. Strogatz // Phys. Rev. Lett., V.93,174102, 2004.

[2] P. Ashwin, O. Burylko // Chaos, V.25, 013106, 2015.[3] L. Larger, B. Penkovsky, Y. Maistrenko // Phys. Rev. Lett.,

V.111, 054103, 2013.[4] Kuramoto Y.Chemical Oscillations, Waves and Turbulence.

Springer, Berlin, 1984.

aSaratov Branch of the Institute of Radio Engineering and Elec-tronics of Russian Academy of Sciences, 38 Zelyonaya Street,Saratov 410019, [email protected]

Experiments on clustering and syn-chronous patterns in a configurable net-work of chaotic oscillators

Soudeh Yaghoutia, Carlo Petrarcaa and Massimilianode Magistrisa

We present new experimental results, on a recentlydeveloped set-up, implementing a dynamically con-figurable network of chaotic oscillators with Chua’scircuits as nodes. The set-up has been designedand tailored to easily perform real time experimentson complex networks with arbitrary topology. Wefocus here on the emergence of symmetry relatedsynchronization patterns, as well as the switchingamong different clusters due to modification of the

15

network structure and/or coupling strength, that areexperimentally analyzed for the first time in such typeof networks. The observed behavior confirm basictheoretical expectations on small networks, as recentlyappeared in literature. The scalability to highercomplexity network, as allowed by the consideredsetup, will be briefly discussed.

aDipartimento di Ingegneria Elettrica e delle Tecnologiedell’Informazione University of Naples FEDERICO II - Via Clau-dio 21, I-80125 Napoli, Italy.soudeh.yaghouti, carlo.petrarca, [email protected]

Prediction of the Indian Summer Mon-soon as a spatially organized criticaltransition

Veronika Stolbovaa,b, Elena Surovyatkinaa,b,c andJurgen Kurthsa,b,d

The prediction of the Indian Summer Monsoononset and withdrawal is a vital question for more thanone billion people. A slight deviation of the monsoontiming as delay (or early arrival) may lead to drasticdroughts (floods) extremely affecting croplands, liveli-hood and prosperity of the inhabitants of the Indiansubcontinent. As the onset of the Indian summermonsoon takes place abruptly, its predictability inadvance (more than two weeks) remains a challenge,despite numerous deduction methods. In our study,we consider Indian Monsoon as a spatially organizedcritical transition from the sporadic rainfall (pre-monsoon state) to spatially organized and temporallysustained rainfall (monsoon state). Using criticalphenomena associated with critical transitions, wedetect areas on the Indian subcontinent sensitiveto the approaching monsoon, and by monitoringdynamics in the detected areas we track arrival ofIndian Summer Monsoon on the Indian subcontinent.Within this framework, we propose an early (morethan one month in advance) predictability scheme forIndian Monsoon onset and withdrawal. Our approachallows to predict the onset date of the Indian SummerMonsoon two weeks earlier and withdrawal date morethan a month earlier than existing methods for theperiod 1965-2015. In addition, our results provideinformation about the influence of El-Nino/SouthernOscillation on the Indian Monsoon in considered year.Our approach opens a perspective for prediction ofcritical transitions advancing in spatially organizedsystems in Climate, Physiology, and Neuroscience.

aPotsdam Institute of Climate Impact Research, P.O.Box601203, 14412 Potsdam, Germany; bDepartment of Physics,Humboldt-Universitat zu Berlin, Newtonstr. 15, 12489 Berlin,Germany; cSpace Research Institute, Russian Academy of Sci-ences, Profsoyuznaya 84/32, GSP-7, Moscow 117997, Russia;dInstitute for Complex Systems and Mathematical Biology, Uni-versity of Aberdeen, Aberdeen AB243UE, [email protected]

Wednesday 9 September11:10-12:25

Room 1: Brain

Robust spatial memory maps in flick-ering neuronal networks: a topologicalmodel

Yuri Dabaghiana,b

The interest on the interaction between neurons andelectrical devices started in 1924, when the humanbrain activity was recorded for the first time. After al-most 100 hears the modern semiconductor technologyis able to produce devices with nano-metrical dimen-sions, which can be used to control and modulate thecells behavior. These new hybrid devices can improvethe therapeutic approach in many pathologies suchas cord injury, epilepsy, Parkinson’s disease. Actuallyjust few theoretical results are available in literature.In this work we will present a simplifed mathematicalapproach to describe the behaviour of a nano-sizedsemiconductor device coupled with a neuronal cellularmembrane. From the mathematical point of view thesemiconductor device is described using the quantumhydrodynamical equation (QHD), whereas the ionsmoving across the cellular membrane, through ionicchannels, are modelled by a modifed version of thePoisson-Nerst-Plank equation (PNP), which is ableto include size exclusion effects. A suitable set ofinterface conditions is presented in order to provethe existence and the uniqueness of the solution.Finally the model is tested numerically on a simplifedgeometry.

aDepartment of Computational & Applied Mathematics, RiceUniversity, Houston, USA; bJan and Dan Duncan NeurologicalResearch Institute, Baylor College of Medicine, Houston, [email protected]

Nonlinear dynamics and low-frequencyfluctuations in network hubs: tenta-tive analogy between the resting hu-man brain and coupled single-transistorchaotic oscillators

Ludovico Minatia,b, Pietro Chiesab, Davide Tabarellib,Ludovico D’Incertic and Jorge Jovicichb

It is well-established that the node degree of struc-tural and functional connectivity in the human brainfollows a scale-free distribution wherein few nodes, re-ferred to as hubs, have a disproportionately high num-ber of links. It however remains less understood ifactivity in such nodes exhibits dynamical propertiesdifferent from the rest of the network. Here, high-temporal resolution resting-state fMRI data from a

16

group of healthy participants were analyzed. Largenode degree of functional connectivity (inter-regionalsynchronization) was strongly associated with i) evi-dence of non-linear structure, manifest as lower cor-relation dimension with clearer dimensional saturationcompared to surrogate data, ii) spectral shift towardslower frequency fluctuations. We speculated that suchfindings could represent an at least partially general-izable relationship, and went on to realize a 90-ringnetwork of diffusively coupled single-transistor chaoticoscillators, in which 4 ‘areas’ were hardwired as hubsthrough addition of long-distance connections. Nearcriticality, transition to chaotic dynamics was selec-tively observed for oscillators in these hub areas, withfindings closely recalling those from brain data. Theseresults are also in accord with meso-scale recordings ofneural cultures performed elsewhere. It appears thatthere may a relationship between network topology andtransition to non-linear, potentially chaotic dynamics,which could hold across very different systems and scalelevels.

aScientific Department and cNeuroradiology Unit, FondazioneIRCCS Istituto Neurologico Carlo Besta, Milan, Italy; bCenterfor Mind/Brain Sciences, University of Trento, [email protected]

A simplifed mathematical model fornano-bio interface

Federica Di Michelea, Bruno Rubinoa and RosellaSampalmieria

The interest on the interaction between neurons andelectrical devices started in 1924, when the humanbrain activity was recorded for the first time. After al-most 100 years the modern semiconductor technologyis able to produce devices with nano-metrical dimen-sions, which can be used to control and modulate thecells behavior. These new hybrid devices can improvethe therapeutic approach in many pathologies such ascord injury, epilepsy, Parkinsonn’s disease. Actuallyjust few theoretical results are available in literature.In this work we will present a simplifed mathematicalapproach to describe the behaviour of a nano-sizedsemiconductor device coupled with a neuronal cellularmembrane. From the mathematical point of view thesemiconductor device is described using the quantumhydrodynamical equation (QHD), whereas the ionsmoving across the cellular membrane, through ionicchannels, are modelled by a modifed version of thePoisson-Nerst-Plank equation (PNP), which is ableto include size exclusion effects. A suitable set ofinterface conditions is presented in order to provethe existence and the uniqueness of the solution.Finally the model is tested numerically on a simplifedgeometry.

aDepartment of Information Engineering, Computer Sciencesand Mathematics, University of L’Aquila - via Vetoio, loc. Cop-pito, I-67100 L’Aquila, Italy.

[email protected]



Modified microwave chaotic Colpitts os-cillator

A. I. Panasa and N. A. Maximova

The report is devoted to the problem of a practicalimplementation of microwave chaotic oscillators. Thisimportant issue is urgent problem because of the needto design energy-efficient sources of ultra widebandmicrowave chaotic signals for wireless devices meetsthe IEEE standards 802.15.4 and 802.15.6. Thechaotic Colpitts oscillator is known as one of thegenerators with a simple structure. It has experi-mentally approved implementations in the microwaverange. A standard oscillator circuit includes anactive element (bipolar transistor) and three externalreactive elements (two capacitors and inductor). Theoscillator implementation, results of the simulationand experiments are presented in the report. Thegeneration of ultra wideband chaotic signals in thefrequency range 1.5 – 6.5 GHz. with the efficiency of2% is shown. On the other hand, a modified schemeof the chaotic Colpitts oscillator is proposed in thereport. It eliminates external capacitors from theoscillator circuit. In this case, the capacitances of p-njunctions of the transistor play the role of externalcapacitors. It is shown, when using BFP620F bipolartransistor as active element the frequency band of thegenerated chaotic signal is increased to 7.5 GHz whilethe efficiency raise up to 7%.

aKotel’nikov Institute of Radio Engineering and Electronics ofRussian Academy of Sciences (Fryazino Branch), 1, Vvedenskogosq., Fryazino, Moscow reg., 141190, Russian [email protected]

Cloning of 3D chimera states

Volodymyr Maistrenkoa, Oleksandr Sudakova, OleksiyOsiva and Yuri Maistrenkoa

In this contribution we propose the method forcloning of 3D chimera states that display a self-organized spatial pattern of coexisting coherence andincoherence for nonlocally coupled oscillators in three-dimensional networks. 3D chimera states were re-ported recently in [1] for a Kuramoto network of N3

identical oscillators

φijk = ω +K

P 3

∑(i′j′k′)∈BP (i,j,k)

sin(φi′j′k′ − φijk − α),

17

i, j, k = 1, ..., N , where φijk are phase variables, in-dexes i, j, k are periodic mod N which induces a 3Dtorus structure on the array. The coupling is assumedto be long-ranged and isotropic: each oscillator φijk iscoupled with equal strength K to all its nearest neigh-bors φi′j′k′ within a range P. i.e. to those oscillatorsfalling in the ball-like neighborhood

BP (i, j, k) := (i′, j′, k′) : (i′ − i)2 + (j′ − j)2 + (k′ − k)2 ≤ P 2

Here the distances i′ − i, j′ − j, and k′ − k are cal-culated regarding the periodic boundary conditions ofthe network. The phase lag parameter α is assumedto belong to the attractive coupling range from 0 toπ/2, the second control parameter is the coupling ra-dius r = P/N . Two large families of the 3D chimerastates: stationary - incoherent/coherent balls, tubes,crosses, layers (I), and scroll waves - incoherent rollsin spirally rotating coherent surround- ing, which aregenerated by random initial conditions, were found [1]in large domains of the parameter space (r, α).

The cloning process of 3D chimera states can bedescribed as follows: we take eight initial conditionsφi0j0k0

of 3D chimera states obtained for N3 oscilla-tors and using periodic boundary condition, build ini-tial conditions 8φi0j0k0 for (2N)3 oscillators, whichgenerate the 3D chimera states clones with doublevalue of N in system (1), and so on indefinitely. Asa result we get multiheaded [2] 3D chimera states withincreasing number of coherence and incoherence partswhere their number of heads tends to infinity whenN → ∞. Examples of 3D chimera states clones ob-tained from original 4 spiral incoherent rolls are pre-sented in Fig.1. We also find stability regions for these3D clones in the parameter space (r, α).

The contribution comprises video presentation il-lustrating the origin and evolution of the 3-Dchimera states. The massive calculations wereperformed at the computer cluster ”CHIMERA”(http://nll.biomed.kiev.ua/cluster).

Fig. 1: Example of 3D chimera state and its clones: (a)

original 4 spiral incoherent rolls (r = 0.12, N = 50), (b) 16

spiral incoherent rolls (r = 0.06, N = 100), (c) 64 spiral

incoherent rolls (r = 0.03, N = 200), (d) 256 spiral incoherent

rolls (r = 0.015, N = 400). Coordinates xi = i/N , yj = j/N ,

zk = k/N , α = 0.7.

[1] Maistrenko Yu., Sudakov O., Osiv O. and Maistrenko V.[2015] “Chimera states in three dimensions”, New Journalof Physics (accepted for publication, provisionally scheduledfor August 2015).

[2] Maistrenko Yu., Vasylenko A., Sudakov O., Levchenko R.and Maistrenko V. [2014] “Cascades of multiheaded chimerastates for coupled phase oscillators”, Int. J. Bif. and Chaos.24, 1440014.

aNational Scientific Centre for Medical and Biotechnical Re-search, NAS of Ukraine, 54, Volodymyrska Str., 01030 Kyiv,

[email protected]

Emergence of complex structure and be-havior from elementary adaptive net-work automata

Daniel Wechslera and Ruedi Stoopa

A variety of real-world systems can be modeled asadaptive networks, that combine an evolving networkwith a dynamical process on that network. Social,transportation and neural networks, for example, mayshow robust self-organization towards a dynamicallycritical state or the formation of complex networktopologies. How, exactly, these system level behaviorsemerge from the local rules governing evolving topol-ogy and node dynamics, is poorly understood. We in-troduce an elementary automaton model that evolvesa network and a dynamical process on it according tosimple local rules to shed light on this problem. Weperform exhaustive simulations of all of our 256 differ-ent possible update rules, allowing a systematic studyof their impact on emerging system level behaviors.The in-depth analysis of an exemplary rule reveals arich interplay between topology and node dynamics,with evidence of critical dynamics and a the emergenceof a complex network topology. Our model may bea promising candidate to investigate the question ofwhether there are general principles that relate the lo-cal rules to the emerging system level behaviors.



Room 1: Brain

Multiplex network based features forearly Alzheimer characterization

Nicola Amorosoa,b, Marianna La Roccaa,b, RosangelaErricoc,d, Annarita Fanizzia, Elena Garuccioe, AnnaMondaa, Sabina Tangarob, Andrea Tateoa and RobertoBellottia,b

Magnetic resonance imaging (MRI) has been ex-tensively studied along with pattern recognition tech-niques to detect signifcant biomarkers for the early di-agnosis of Alzheimers disease (AD). Features involvingeither the whole brain or local regions of interest re-lated to the disease bring substantially complementaryinformation about the pathology. Brain scans natu-rally define connectivity networks among the several

18

regions a brain can be parcellated in. Accordingly, (i)we studied how multiplex networks can supply a conve-nient mathematical framework to describe AD patternsof disease in terms of features modeling the structuralinter and infra subject brain connectivity. (ii) We usedFreeSurfer to perform volume based morphometry anduse it to assess the method performances. We studied aset of 100 structural T1 brain scans from subjects of theAlzheimers Disease Neuroimaging Initiative includingAD patients, normal controls (NC) and mild cognitiveimpairment (MCI) subjects. Finally, we evaluated theclassification performances including the comparison oftwo state-of-the-art classification techniques, RandomForests and Support Vector Machines. The experi-mental results, obtained with a 5-fold cross validation,showed that classification performances could be sig-nificantly improved with the use of multiplex networkbased features.

aUniversita degli Studi di Bari “Aldo Moro”, 70126 Bari, Italy;bIstituto Nazionale di Fisica Nucleare, sez. di Bari, Italy;cIstituto Nazionale di Fisica Nucleare, sez. di Genova, Italy;dUniversita degli studi di Genova; eUniversita degli studi [email protected]

Simple analog electronic model of a spik-ing neuron featuring short- and long-term memory, and inhibitory/excitatorysynaptic-like behavior

Guillermo V. Savinoa

This paper presents an analogue discrete electroniccircuit implementation of a neuron model with manysynaptic like connections. The single neuron cell cir-cuit synapses and the soma make use of an unusualreversal bipolar transistor (BJT) connection. It has acompact layout and very low energy consumption, inthe range of 10 microJoule per spike. Experimentalresults show the capability of the circuit to generateperiodic spikes that are triggered delayed (inhibitory)or advanced (excitatory) in response to synaptic-likeexternal excitations and/or its own activity (synapticweight). The circuit dynamic includes a self generatedlong-term soma memory and a short-term synapticmemory. The synapse number can be increases, froma minimum of two transistors, just adding as many astransistors as desired. Hence, the circuit provides afoundation or building block for designing massivelyparallel analogue, small silicon area and power con-sumed neuromorphic or any specific application VLSIintegrated neural networks.

aUniversidad Nacional de Tucuman, [email protected]

Complex network for DRD2 gene com-munity identification in Schizophrenia

Anna Mondaa, Nicola Amorosoa,b, AlessadroBertolinod, Giuseppe Blasic, Pasquale Di Carloc,Marco Papalinoc, Giulio Pergolac, Sabina Tangarob,Andrea Tateoa and Roberto Bellottia,b

In this work we used topological features of geneco-expression networks to pin down the relation-ships between genes related to a specific disease. Weadopted a graph theory framework to investigate a ge-netic co-expression module previously associated withschizophrenia in 199 non-psychiatric subjects. Weidentified communities of co-expressed genes, combin-ing the study of basic topological properties, such asde- gree and betweenness, and assessed the method ro-bustness in several cross-validation configurations. Wefound a small and stable community of genes interact-ing with DRD2, whose relevance in schizophrenia is acutting edge research theme. The detected communitypreserves the information essential to understand thedynamic of the genetic process. By investigating theneurophysiological correlates of genetic variants asso-ciated with this community we found that this tech-nique outperformed previous procedures to identifygenetic markers of schizophrenia-related phenotypes.Thus, topological features of gene co-expression net-works are critical for marker detection.

aInter-University Physics Department “Michelangelo Merlin”,Universita degli Studi di Bari “Aldo Moro”, 70126 Bari, Italy;bIstituto Nazionale di Fisica Nucleare, sez. di Bari, Italy;cDepartment of Basic Medical Sciences, Neuroscience and SenseOrgans Universita degli Studi di Bari “Aldo Moro”, 70124 Bari,Italy; dpRED, NORD DTA, F. Hoffman-La Roche Ltd., 4070Basel, [email protected]

Stabilization of steady states in an arrayof the coupled FitzHugh–Nagumo oscil-lators

Arunas Tamaseviciusa, Elena Adomaitienea, GytisMykolaitisa and Skaidra Bumelienea

A well known phenomenon in nonlinear dynamics isthat dynamical behavior of a system can be changedby means of applying external periodic force. Specifi-cally, high frequency forcing can change the stabilityproperties of the inherent steady states. An example isthe stabilization of the unstable upside-down positionof a mechanical pendulum by vibrating its pivot upand down at a relatively high frequency. Recently this“mechanical” idea has been successfully exploited [1]in a seemingly unexpected area, namely to explainthe mechanism of the so-call deep brain stimulation(DBS), conventionally used to avoid the tremor forpatients with the Parkinson disease. Unfortunately,the common DBS treatment is often accompaniedwith unpleasant and dangerous side effects, since itrequires permanent high frequency high amplitude

19

current injection into the brain. We suggest to exploitthe tracking filter technique (TFT) for suppressingneuronal oscillators in an array of coupled cellsand compare it with the commonly used DBS. Theinvestigations have been carried out with an array ofthirty electronic FitzHugh–Nagumo type oscillators.We demonstrate that the TFT has and advantage overthe DBS in the sense that the controlling forces arevanishing.

[1] K. Pyragas, V. Novicenko, P.A. Tass, Biol. Cybern. 107,669 (2013).

aDepartment of Electronics, Center for Physical Sciences andTechnology, LT-01108 Vilnius, [email protected]



Ultrawideband chaotic transmitter panel

Yu.V. Andreyeva and A.S. Dmitrievb

Due to severe restrictions on power spectral density(-41/3 dBm/MHz) [1], ultrawideband (UWB) commu-nication systems of 3-10 GHz frequency range are in-tended to be short-distance (10 to 30 m), local andpersonal-area devices. Yet first tests indicate increas-ing demand for longer-range UWB applications. Whilethe obvious way to increase the distance range is to in-crease the transmitter emission power, this mehod islimited by the above restriction, i.e., in the whole 3-10GHz band the total emission power must not exceed600 mW. However, this restriction pertains only to thepower of individual transmitter. Here we propose tocombine the energy of many transmitters in order tostep over this restriction and to flexibly control thedistance of communications. This goal can easily beachieved with chaotic UWB communications systems(direct chaotic communications), in which informationis encoded with a sequence of ultrawideband chaoticradio pulses [2, 3]. The idea is to organize collec-tive simultaneous emission of chaotic radio pulses pro-duced by chaotic oscillators of individual transmitters(Fig. 1). Since the UWB oscillators are independent(and the receiver is noncoherent), their chaotic signalsare uncorrelated and are summed by power at the re-ceiver input, so that the signal power of an ensembleof N transmitters is N times the power of an individualtransmitter. In this report we investigate the proper-ties of chaotic transmitter panel, i.e., an array of UWBtransmitters with independent UWB chaotic oscilla-tors, which are synchronized by LF information signal,so that all transmitters emit chaotic radio pulses at thesame time, each with its own antenna. The panel prop-erties are studied in numerical simulation as well as in

physical experiment. The panel is shown to be an effi-cient method for increasing communication range; andunlike antenna arrays, due to the use of uncorrelatedchaotic signals the panel does not add directivity tothe emission pattern.

Fig. 1: Block diagram of UWB chaotic transmitter panel.

[1] Federal Communications Commission (FCC), “Revisionof Part 15 of the Commission’s Rules Regarding Ultra-Wideband Transmission Systems”, First Report and Order,ET Docket 98-153, FCC 02-48; Adopted: February 14, 2002;Released: April 22, 2002.

[2] Dmitriev A.S., Panas A.I., and Starkov S.O. Direct ChaoticCommunication in Microwave Band // Electronic NonLinearScience Preprint, nlin.CD/0110047.

[3] Dmitriev A.S., Hasler M., Panas A.I., and ZakharchenkoK.V. Basic principles of direct chaotic communications //Nonlinear Phenomena in Complex Systems, 2003, vol. 6, no.1, pp. 488-501.

aMoscow Institute of Physics and Technology (State University);bKotelnikov Institute of Radio Engineering and Electronics [email protected]

Frequency-sharpening and scale-invariance in a system of forcing-coupledHopf oscillators

Florian Gomeza, Tom Lorimera and Ruedi Stoopa

Traditionally, the study of coupled oscillators in-volves elements that intrisically oscillate even when un-coupled, such as Kuramoto oscillators [1]. However,many systems, especially in biology, are composed ofelements that are found to be in an excitable state,below the threshold to oscillation. This state is char-acterized by its vicinity to a bifurcation, typically ofsaddle-node or Andronov-Hopf type. Motivated by re-cent results from the modeling of sound processing inthe mammalian cochlea, we look at a system of forcing-coupled sub-threshold Hopf oscillators. This system isshown to exhibit a higher-level Hopf bifurcation, wherethe coupling strength acts as the bifurcation parame-ter. In particular, the proximity to the higher-levelbifurcation gives rise to a frequency sharpening of theresponse to external input. Moreover, we show thatthis coupled system can effectively be described by asingle Hopf oscillator. This scale-invariance corrobo-rates the mesoscopic Hopf modeling approach to hear-ing systems.

[1] S.H. Strogatz, From Kuramoto to Crawford: exploring theonset of synchronization in populations of coupled oscillators.Physica D 143, 1-20 (2000).


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Recovery of couplings and parameters ofelements in networks of time-delay sys-tems

Mikhail Prokhorova, Vladimir Ponomarenkoa and IlyaSysoeva

The problem of detecting the presence, structure,and characteristics of couplings in various networksfrom their time series has attracted a lot of atten-tion in recent years. To solve this problem a variety ofmethods has been proposed including Granger causal-ity, phase dynamics modeling, and adaptive feedbackcontrol. However, in most of studies, either the net-work elements were without time-delayed feedback orthe delays were assumed to be known in advance.

A method for estimating both the network connec-tivity and node parameters including the delay timefor networks of time-delay systems has been proposedby us recently in [1]. It is based on the reconstructionof model delay-differential equations for the networkelements and the diagnostics of statistical significanceof couplings. However, the problem of network recon-struction is solved in this method in two steps. At first,the delay time of each element in the network is recov-ered. Then, other parameters and nonlinear functionsof the elements and coupling architecture are recon-structed. Moreover, the results of coupling recoverysometimes depend on the choice of the initial couplingdistribution used in the procedure of reconstruction.

In the present paper, we propose a method for recon-structing the parameters of elements and architectureand strengths of couplings in networks of time-delaysystems which is devoid of the above mentioned draw-backs and is more quick-operating than the iterativemethod in [1]. The proposed method is based on theminimization of the objective function which charac-terizes the distance between the points of the recon-structing nonlinear function ordered with respect tothe abscissa. This minimization is carried out for dif-ferent trial delay times chosen from some interval. Theglobal minimum of the objective function is observedat the true choice of the delay times. To separate therecovered coupling coefficients into significant and in-significant ones we use the method of K-means.

The proposed method can be applied to the net-works composed of diffusively coupled time-delay sys-tems, each described by the equation

xi (t) =− xi (t) + fi (xi (t− τi))

+

M∑j=1(j 6=i)

ki,j (xj (t)− xi (t)),

where i = 1, . . . ,M, M is the number of elementsin the network, τ i is the delay time, fi is a nonlinearfunction, and ki,j are the coupling coefficients charac-terizing the strength of influence j → i, i.e., from thejth element to the ith one.

We verified the method by applying it to chaotictime series produced by model equations of the network

composed of sixteen diffusively coupled Ikeda equationsin the presence of noise. The parameter values of allcoupled Ikeda equations were different. The cases ofcomplicated coupling architecture are considered. Itis shown that the method allows us to recover accu-rately the coupling architecture and delay times of allelements. The other parameters and nonlinear func-tions of Ikeda equations are reconstructed with a highaccuracy.

The method is also successfully applied to experi-mental time series obtained from a ring of ten electronicoscillators with delayed feedback coupled by resistors.

[1] I.V. Sysoev, M.D. Prokhorov, V.I. Ponomarenko, B.P.Bezruchko “Reconstruction of ensembles of coupled time-delay systems from time series”, Phys. Rev. E, 2014, V.89,062911.

aSaratov Branch of the Institute of Radio Engineering and Elec-tronics of Russian Academy of Sciences, 38 Zelyonaya Street,Saratov 410019, [email protected], [email protected]

Power laws as the result of exponentiallydecaying spiking frequency during syn-chronized activity

Damian Bergera and Ruedi Stoopa

Neuronal activity, measured in in vitro and invivo experiments, can exhibit spontaneous burstsof spikes, followed by periods of reduced activity.Several experiments showed that the bursting periodsconsist of distinct spatiotemporal patterns, so calledavalanches, with a size distributed according to apower law. In order to explain the power laws in theneuronal avalanche size distributions, comparisons tocritical branching processes and second order phasetransitions have been made. Here we present evidencefor a simpler process that may lead to the power lawin the avalanche size distribution. We studied in vitrothe activity of dissociated hippocampal rat neurons.For both the avalanche size distribution and theinter-event interval distribution we found power laws.Additionally we observed that the activity withinisolated bursts decays exponentially. We consequentlymodeled bursts by an exponentially decaying spikingprobability and found avalanche size and inter-eventinterval distributions that are well-modeled by powerlaws and reflect our biological data very well. Wefound the power law exponent generated by our modelanalytically for the inter-event interval case, whichshows very good agreement with the biological data.


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Thursday 10 September11:10-12:25

Room 1: Control

Quantum transport in light-harvestingsystems

Fausto Borgonovia

Natural photosynthetic systems interact with dif-ferent environments, which are a source of noise butcan also induce cooperative coherent effects, such assuperabsorption of light and supertransfer of excita-tion. Both cooperativity and noise can be essential toachieve efficient energy transport in natural complexesand in bio-inspired quantum devices. We show thispoint with the aid of the non Hermitian Hamiltonianapproach to open quantum systems and analyzingboth general quantum disordered networks and realis-tic models of photosynthetic antenna complexes (suchas LHI, FMO).

aDepartment of Mathematics and Physics, Catholic University,Brescia, [email protected]

Transport and non-equilibrium dynam-ics with cold atoms

Sandro Wimbergera

State-of-the-art experiments with ultracold atomsand molecules allow for an unprecedented control ofmicroscopic degrees of freedom and the bottom-upconstruction of nano-structures in various regimes(glasses, crystals, superfluids). In close collaborationwith experiments, we propose to create structuresconsisting of a few hundred to a few million particles,covering the cross-over from microscopic to macro-scopic matter. We focus hereby on both the productionof stable many-body structures, such as static latticesmimicking magnetic materials or coherent solitonsin optical lattices [1], as well as on quantum trans-port problems. The dynamics of ultracold fermionsand bosons simulates the transport of electrons insolids, with the great advantage of unprecedentedexperimental control and in situ observation possibil-ities [2]. New forms of current transport, includingmaterials with negative differential resistivity [3],driven by many-body correlation effects have beenobserved already. This opens many frontiers for thedesign of matter and the control of currents [4,5] onthe verge between the quantum and the classical world.

[1] G. Kordas, S. Wimberger, D. Witthaut, EPL 100, 30007(2012).

[2] G. Kordas, D. Witthaut, S. Wimberger, Non-equilibriumdynamics in dissipative Bose-Hubbard chains, Ann. Phys.

(Berlin), available online: DOI: 10.1002/andp. 201400189(2015).

[3] R. Labouvie, B. Santra, S. Heun, S. Wimberger, H. Ott,arXiv:1411.5632 (preprint 2015).

[4] Atom-based analogues to electronic devices, EurophysicsNews 44, 6, 20 (2013), highlighting: G. Ivanov, G. Kordas,A. Komnik, S. Wimberger, Eur. Phys. J. B 86, 345 (2013).

[5] Stromubertragung auf atomarer Ebene, Newspaper article inthe Rhein-Neckar-Zeitung (Heidelberg, Germany), 9/4/2014.

aDiFeST, Universita degli Studi di Parma, [email protected]

Thermal conduction and thermoelectric-ity in one-dimensional nonlinear systems

Shunda Chena,b, Jiao Wangc, Giulio Casatia,d andGiuliano Benentia,b

Deriving the empirical Fourier heat conduction lawfrom microscopic dynamics is an old but still challeng-ing problem. We study in one-dimensional momentum-conserving nonlinear systems, how nonintegrable dy-namics may affect thermal transport properties [1]. Wefind that when the system is close to integrable limit,the heat conductivity may keep significantly unchangedover a certain range of the system size, and as the sys-tem tends to integrable limit, the range of this Fourier-like behavior may expand rapidly. These results estab-lish a new connection between the macroscopic thermaltransport properties and the underlying dynamics. Anapplication of the Fourier-like behavior to thermoelec-tric transport of nonlinear interacting particles is alsodiscussed [2].

[1] S. Chen, J. Wang, G. Casati and G. Benenti, Nonintegrabil-ity and the Fourier heat conduction law, Phys. Rev. E 90,032134 (2014).

[2] S. Chen, J. Wang, G. Casati and G. Benenti, Thermo-electricity of interacting particles: A numerical approach,arXiv:1506.06022.

aCenter for Nonlinear and Complex Systems, Universita’ degliStudi dell’Insubria, Como, Italy; bIstituto Nazionale di FisicaNucleare, Sezione di Milano, Italy; cDepartment of Physics andInstitute of Theoretical Physics and Astrophysics, Xiamen Uni-versity, China; dInternational Institute of Physics, Federal Uni-versity of Rio Grande do Norte, Natal, [email protected]



Cellular neural networks based emula-tion of analog filters: theory and designprinciple

Nkiediel Alain Akwira, Jean Chamberlain Chedjoua

and Kyandoghere Kyamakyaa

22

We develop and validate through some illustrativeexamples an efficient concept based on cellular neuralnetworks for the synthesis of analog filters. Severaltypes of filters (i.e. Low-pass, High-pass, Band-pass,and Band-stop) are envisaged each of which is emu-lated in the form of the CNN mathematical model.The resulting coefficients of the CNN mathematicalmodel (called CNN templates) are derived for eachtype of filters. Correspondences are establishedbetween the parameters of the CNN mathematicalmodel and the physical components (i.e. resistors,capacitors, inductances, op-amps, etc.) of the filters.The key contribution of this work is to demonstratethe potential of using cellular neural networks (CNN)as a universal concept for analog filters modelling andsimulation. The main motivation of developing theCNN- concept for the emulation of analog filters isjustified by its excellent features (e.g. high flexibility,good stability, and high accuracy). Further, theCNN-concept developed is a framework which canbe efficiently used for a straightforward conversion ofanalog filters into digital filters.

aInstitute of Smart System Technologies, Transportation Infor-matics Group (TIG), Universitat Klagenfurt, Klagenfurt, [email protected]

Experimental investigation of chaos syn-chronization in nonlinear oscillators viacyclic coupling

O.I. Olusolaa, A.I. Egunjobib, A.N. Njaha and S.K.Danac

This paper investigates chaos synchronization in ex-perimental circuits using Sprott, Rossler and van derPol oscillators as paradigmatic oscillators. Using mul-tiSIM 12.0 software the threshold coupling is first de-termined when complete synchronization (CS) is ob-served via bidirectional and cyclic mutual coupling aswell. MultiSIM simulation results are experimentallyverified using off-the-shelve electronic components in abreadboard. It is found that, by applying cyclic cou-pling in some of the variables, it is possible to syn-chronize two oscillators where the conventional bidi-rectional coupling failed to achieve. Furthermore, it isfound that the synchronization behaviour can be en-hanced by applying cyclic coupling to a selected set ofvariables of the oscillators at least for the model sys-tems considered here.

aDepartment of Physics, University of Lagos, Akoka, Lagos,Nigeria; bFederal University of Agriculture, Abeokuta, Nigeria;cCSIR-Indian Institute of Chemical Biology, 4, Raja S.C. Mul-lick Road, Kolkata 700032, [email protected]

A novel recurrent neural network basedultra-fast, robust and scalable solver fortime varying matrix inversion

Vahid Tavakkolia, Jean Chamberlain Chedjoua andKyandoghere Kyamakyaa

Various algorithms exist to solve matrix inversion.Most of them are very good algorithms however, whichcould be implemented only on single processor comput-ers. This makes these algorithms becoming inefficientwhen trying to implement them on multi-processorplatforms. The main root of the problem lies in the na-ture of the algorithms as they are essentially designedto be used on single processors. Hence, the search fornew algorithms that fit better for implementation onparallel systems is necessary. Using parallel computingframeworks like neural networks can provide a goodbasis to support algorithms or concepts highly com-patible with parallel platforms and thereby ensuring alow implementation cost. In this paper, we do suggestand demonstrate a new way of solving linear algebraicequations using a Cellular Neural Network (CNN) Pro-cessor. Although similar works have been performedby using different types of Neural Networks such asRecurrent Neural Network (RNN) and Artificial Neu-ral Network (ANN) the fact of developing novel RNNmethods constructed on CNN- platforms to solve ma-trix inversion does increase convergence speed and pro-vide feasible solutions for an implementation on analogprocessors.

aInstitute for Smart Systems Technologies, Klagenfurt Univer-sity, Universitatsstraße 65-67, A-9020 Austria.vtavakko,kyandoghere.kyamakya,[email protected]


Room 1: Synchronization

Phase and frequency locking in complexmodel of blood pressure dynamics

A.S. Karavaeva,b, Y.M. Ishbulatovb, V.I.Ponomarenkoa,b and M.D. Prokhorova

Construction of mathematical models of the real-world complex systems is an important part of theirinvestigation. Using the adequate models one can bet-ter understand the system operation and predict itsbehavior in time and under parameter variation. It al-lows one to obtain new fundamental knowledge aboutthe structure of the studied complicated systems andcomprehend the features of their individual and collec-tive dynamics.

In the present study we propose a model for descrip-tion of the complex blood pressure dynamics. The

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model simulates the operation of sinus node and its fre-quency modulation by the signals of autonomous con-trol system, models the baroreflex regulation of meanarterial pressure, and takes into account the influenceof respiration. The structure of the proposed modelof cardiovascular system is chosen similarly to the oneproposed by Kotani K. et al [1]. To simulate the barore-flex regulation of mean arterial pressure we use themodel of self-oscillating time-delayed feedback oscilla-tor [2]. We consider various types of introducing therespiration into the model. The influence of dynamicaland measurement noises on the observed dynamics ofthe model is taken into account.

The obtained results indicate that including ofnonautonomous time-delayed feedback oscillator intothe model results in much better qualitative and quan-titative coincidence of the model cardiointervalogrampower spectra with those observed for the real signals.In particular, the model power spectra exhibit clearlydistinguished peaks corresponding to the frequencies ofthe regulatory systems activity as well as in the powerspectra of experimental cardiointervalograms [3].

Moreover, the proposed model demonstrates forthe first time the phenomena of phase and frequencylocking of the regulatory system slow oscillations bythe respiration that is typical for the real cardiores-piratory dynamics. It is shown that the system ofbaroreflectory regulation of mean arterial pressurecould be synchronized by the signal of respirationwith linearly increasing frequency similarly to thesynchronization of radio technical oscillator by theexternal signal. Analogous effect has been observedearlier in our experimental study of healthy subjects[4].

[1] Kotani K. et al // Phys. Rev. E, V.72, 041904 (2005).[2] Ringwood J.V., Malpas S.C. //. Am. J. Phys. Regul. In-

tegr. Comp. Phys. V.280, R1105-R1115 (2001).[3] Billman G.E. // Frontiers in Physiology V. 2:86, P.1-13

(2011).[4] Karavaev A.S. et al. // Chaos, V.19, 033112 (2009).

aSaratov Branch of the Institute of Radio Engineering and Elec-tronics of Russian Academy of Sciences, Zelyonaya Street 38,Saratov 410019, Russia; bDepartment of Nano- and BiomedicalTechnologies, Saratov State University, Astrakhanskaya Street83, Saratov 410012, [email protected]

A spin physics-based framework for hy-brid recommendation systems

Thomas Otta, Thomas Eggela, Roland Gassmanna,Erich Zbindena and Michael Reinholdb

Recommendation systems guide and support usersin the process of finding relevant items, such as prod-ucts or services, in a potentially huge space of options.There are different schemes upon which recommen-dation systems are based such as collaborative filter-ing [1], content-based filtering [2] or knowledge-basedsystems [3]. Each scheme comes along with certain

strengths and weaknesses, depending on the applica-tion context and the available data. Hybrid systemstry to take advantage of different schemes by combin-ing them. They often show better performance thansingle schemes [4,5]. We report on the developmentof Dayzzi.com, a broker recommendation platform forthe business of promotional items. The developmenthas been facing the challenges of data sparsity, limitedavailability of ex-ante user data and a relatively smallnumber of user activities or transactions over time. Toovercome this, we developed a specific knowledge-basedsystem that incorporates the market expertise in theform of sales agents’ thorough understanding of cus-tomer needs and purchasing behavior [6]. The coreprocess of the engine comprises (1) a mapping from aset of variables that characterize the user’s preferencesto a set of hidden variables, akin to a feature selec-tion or dimensionality reduction procedure, and (2) aBayesian classifier to identify relevant items. In orderto increase the learning aptitude of the system based ona hybridization with other recommendation schemes,we reformulate the original scheme in terms of a systemof uncoupled Ising spins that are exposed to variablemagnetic fields. This framework allows us to easily addand combine recommendation schemes in the form ofmagnetic field components, while keeping the advan-tage of having no direct coupling between the recom-mendations of products. This leads to a form of mixedhybridization and keeps the learning process simplerthan in similar approaches, e.g. based on Boltzmannmachines [5].

We explain the construction of the framework and itsmagnetic field components in more detail and illustrateits advantages in comparison to non-hybrid solutions.Furthermore, we report on some implementation issuesregarding recommendation platforms for small andmedium-sized enterprises such as Dayzzi.com, point-ing out the quest for specific approaches in the case ofspecific e-business situations with, e.g., a rather smallnumber of transactions.

[1] J. Bobadilla, A. Hernando, F. Ortega, J. Bernal. A frame-work for collaborative filtering recommender systems. ExpertSystems with Applications, 38, pp. 14609–14623, 2011.

[2] P. Lops, M. de Gemmis, G. Semerraro. Content-based Rec-ommender Systems: State of the Art and Trends. In Recom-mender Systems Handbook, pp. 73–105, F. Ricci et al. (eds),2011.

[3] R. Burke. Knowledge-Based Recommender Systems. In En-cyclopedia of Library and Information Systems, Vol. 69, A.Kent. (ed), 2000.

[4] R. Burke. Hybrid Recommender Systems: Survey and Ex-periments. User Modeling and User-Adapted Interaction, 12,pp. 331-370, 2002.

[5] A. Gunawardana, C. Meek. A Unified Approach to BuildingHybrid Recommender Systems. Proceedings of ACM Inter-national Conference on Recommender Systems, pp. 117-124,2009.

[6] M. Reinhold, S. Reinhold. Data-driven Intelligence for SMEE-Business: A Marketing and Sales Perspective. MarketingReview St. Gallen, 60, pp. 52-59, 2014.

aZHAW Zurich University of Applied Sciences, Switzerland;bUniversity of St. Gallen, [email protected], [email protected]

24

Controlling the range of a Schmitt trig-ger’s switching oscillations by means ofexternal noise and nonlinear feedback

G.A. Zarzaa, S.E. Mangionia, L. Vassalloa and R.R.Dezaa

Recently, one of us has shown numerically that itis possible to confine—by means of a suitably tai-lored multiplicative external noise—the response of abistable system within beforehand-established bounds[1]. Figure 1 shows that when a simple bistable sys-tem like u (1 − u2)—whose stationary pdf is depictedin red—is submitted to multiplicative Gaussian whitenoise, namely ∂tu = u (1 − u2) + Γ1/2(u) η(t) with〈η(t)η(t′)〉 = 2λ2 δ(t− t′) and

Γ =

exp[2b (|u| − ul)] if |u| < ul,

1 if |u| > ul,

the system’s response becomes confined (blue curves).So astounding a result was worth confirming throughan experiment. By means of filters, we have trimmedthe external noise’s bandwidth down to the rangein which the Schmitt trigger’s hysteresis cycle is notstrongly frequency-dependent, and we have devised acircuit featuring nonlinear feedback whose behavior inSpice simulations (Fig. 2) shows the same qualitativefeatures as the numerical simulations. We are now un-dertaking the real experiment, whose definitive reultswill be communicated at the Conference.

Fig. 1: Stationary probability (Pst) vs. u and λ. Red curve:

λ = .02 and b = 0. Blue curves: b = 20. The ul = ±.7 lines are

the chosen confinement bounds.

[1] S. E. Mangioni, “Systems confined by pusher multiplicativenoises”, Eur. Phys. J. B 88, 53–58 (2015)

aIFIMAR (UNMdP-CONICET), Mar del Plata, [email protected]



Fig. 2: Spice simulation of the devised nonlinear circuit.

Continuous and differentiable approxi-mation of a TaO memristor model forrobust numerical simulations

Alon Ascolia, Ronald Tetzlaffa and Leon Chuab

The interest on the interaction between neurons andelectrical devices started in 1924, when the humanbrain activity was recorded for the first time. After al-most 100 hears the modern semiconductor technologyis able to produce devices with nano-metrical dimen-sions, which can be used to control and modulate thecells behavior. These new hybrid devices can improvethe therapeutic approach in many pathologies such ascord injury, epilepsy, Parkinsonn’s disease. Actuallyjust few theoretical results are available in literature.In this work we will present a simplifed mathematicalapproach to describe the behaviour of a nano-sizedsemiconductor device coupled with a neuronal cellularmembrane. From the mathematical point of view thesemiconductor device is described using the quantumhydrodynamical equation (QHD), whereas the ionsmoving across the cellular membrane, through ionicchannels, are modelled by a modifed version of thePoisson-Nerst-Plank equation (PNP), which is ableto include size exclusion effects. A suitable set ofinterface conditions is presented in order to provethe existence and the uniqueness of the solution.Finally the model is tested numerically on a simplifedgeometry.

aInstitut fur Grundlagen der Elektrotechnik und Elektronik,Technische Universitat Dresden, Dresden, Deutschland;bDepartment of Electrical Engineering and Computer Sciences,University of California Berkeley, Berkeley, California, USA.alon.ascoli,[email protected],[email protected]

Ultrawideband microwave 3-7 GHzchaotic oscillator implemented as SiGeintegrated circuit

E.V. Efremovaa and A.S. Dmitrieva

Microwave chaotic oscillations are a promising

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information carrier for ultrawideband communicationsystems [1,2]. The possibility of a wide use of such acarrier type depends on succesful solution of the keytask - creation of small, energy-efficient generatorsof chaotic oscillations. By this moment, a set ofdiscrete-component chaotic oscillators is developed,with characteristics sufficient for ultrawideband com-munication systems [3-5]. However, the developmentlevel of modern communications calls for implemen-tation of such devices using elements of modernsolid-state electronics, i.e., monolithic integratedcircuits. In this report, creation of such devicesis demonstrated on example of microwave chaoticgenerator on silicon-germanium (SiGe) technology.A structure of chaotic generator is proposed thatprovides chaotic oscillations with a required form ofsignal spectrum. A model system on 0.25 micronSiGe process component library is developed, andIC layout is designed. An experimental sample ofmicrowave chaotic source with bipolar transistor asthe active element is fabricated on SiGe 0.25 micronprocess. Operation modes of this integrated circuitare investigated. The system demonstrates generationof ultra-wideband chaotic oscillations of the frequencyrange 3-7 GHz. Results of numerical simulation andexperimental study of the chip are analyzed. Charac-teristics of the integrated-circuit chaotic oscillator arecompared with those of a similar discrete-componentgenerator.

[1] IEEE Standard for Information technology-Telecommunications and information exchange betweensystems-Local and metropolitan area networks-Specificrequirements; Part 15.4: Wireless Medium Access Control(MAC) and Physical Layer (PHY) Specifications forLow-Rate Wireless Personal Area Networks (WPANs);Amendment 1: Add Alternate PHYs, 2007.

[2] IEEE 802.15.6-2012. IEEE Standard for Lo-cal and metropolitan area networks - Part15.6: Wireless Body Area Networks 2012.http://standards.ieee.org/about/get/802/802.15.html

[3] Dmitriev A.S., Efremova E.V., Maksimov N.A., GrigorievYe.V. “Generator of microwave chaotic oscillations based ona self-oscillating system with 2.5 degrees of freedom” // Jour-nal of Communications Technology and Electronics, 2007, V.52, No. 10, P. 1137-1145.

[4] A.S. Dmitriev, E. V. Efremova, N. V. Rumyantsev “A mi-crowave chaos generator with a flat envelope of the powerspectrum in the range of 3-8 GHz” // Technical Physics Let-ters, 2014, V. 40, No., P. 48-51.

[5] Efremova E.V. “Generator of 3-10 GHz ultrawideband mi-crowave chaos” // Proc. 21th Int. Conf. Nonlinear Dynam-ics of Electronic Systems (NDES), Bari, Italy, 10-12 July2013.

aKotelnikov Institute of Radio Engineering and Electronics ofRAS, Moscow Institute of Physics and Technology (State Uni-versity), [email protected]

Cryptanalysis of a random number gen-erator based on a chaotic oscillator

Salih Erguna

This paper introduces an algebraic cryptanalysisof a random number generator (RNG) based on achaotic oscillator. An attack system is proposed todiscover the security weaknesses of the chaos-based

RNG. Convergence of the attack system is provedusing master slave synchronization scheme wherethe only information available are the structure ofthe RNG and a scalar time series observed from thechaotic oscillator. Simulation and numerical resultsverifying the feasibility of the attack system are given.The RNG does not fulfill NIST-800-22 and Diehardstatistical test suites, the previous and the next bitcan be predicted, while the same output bit sequenceof the RNG can be reproduced.

aERARGE - Ergunler Co., Ltd. R&D Center, [email protected]

Poster Abstracts

Search accuracy improvement in artworkretrieval based on similarity of touch

Hiroya Kawaaia and Yuko Osanaa

Recently, some similarity-based image retrieval sys-tems using neural networks which make use of flexi-ble and soft information processing ability of the neu-ral networks have been proposed. However, most ofthe conventional similarity-based (content-based) im-age retrieval systems deal with only scenery image,landscape photographs and so on. In this paper, wepropose an artwork retrieval based on similarity oftouch by self-organizing map with refractoriness. Thissystem is based on the artwork retrieval based on simi-larity of touch [1]. In this system, the number of colors,color information, outline information, LBP (Local Bi-nary Patterns) [3] and so on are used as the imagefeatures. In the proposed system, some new featuressuch as histogram of saturation and brightness, LBPand so on are introduced in order to improve searchaccuracy.

The proposed image retrieval system is based on theself-organizing map with refractoriness [2], and it hasthe input layer and the map layer. The input layer iscomposed of three parts corresponding to (1) the num-ber of colors, (2) color information, (3) outline infor-mation and (4) LBP. And each stored image is trainedto correspond to one of the neuron in the map layer.In the proposed system, the feature vector for the keyimage is given to the neurons in the input layer as thequery, and the neurons corresponding to the imageswhich have similar touch fire sequentially.

In this experiment, we used the proposed systemwhich memorizes 500 images which can be divided into25 groups based on the similarity of touch. Figure 1shows a part of the retrieval results of the proposedsystem. In this figure, top four images which are re-trieved are shown. Table 1 shows F -measure of theproposed system and conventional system [1].

[1] K. Kadokura and Y. Osana: “Image (artwork) retrievalbased on similarity of touch by self-organizing map with

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Fig. 1: Retrieval Results.

Table 1: F -measures.

refractoriness”, Proceedings of International Symposium onNonlinear Theory and its Applications, Luzern, 2014.

[2] T. Ojala, M. Pietiainen and D. Harwood: “A comparativestudy of texture measures with classification based on distri-butions”, Pattern Recognition, Vol. 29, No. 1, pp. 51-59,1996.

[3] H. Mogami, M. Otake, N. Kouno and Y. Osana: “Self-organizing map with refractoriness and its applicaiton to im-age retrieval”, Proceedings of IEEE and INNS InternationalJoint Conference on Neural Networks, Vancouver, 2006.


Fault tolerant adaptive control and syn-chronization of linearizable chaotic sys-tems using RBF neural network andfeedback linearization second order slid-ing mode control

Baraka Olivier Mushagea, Jean Chedjou Chedjoua andKyandoghere Kyamakyaa

This paper addresses the design of adaptive con-trollers for linearizable nonlinear systems, especiallychaotic ones, subject to external disturbances, un-known system parameters changes and actuator faults.The design approach utilises the Input-Output Feed-back Linearization technique combined with the Sec-ond Order Sliding Mode Control approach. A RadialBasis Function Neural Network is used in order to ap-proximate the unknown nonlinear function associatedwith the unknown system parameters. For compen-sating the effects of the external disturbances and theactuator faults for which the upper bounds are un-known, a dynamic switch-gain is used in the Sliding

Mode Controller. The Lyapunov method is used to de-rive the update rules for the switch-gain and for theNeural Network, and to study the closed loop systemasymptotic stability. Compared with existing works,the key achievements in this paper are related to thefact that: (a) no knowledge of the upper or/and lowerbounds of the uncertainty in the system dynamics,external disturbances and actuator faults is requiredfor the controller design; (b) there is a possibility ofachieving successful complete synchronization of twonon-identical chaotic systems or controlling high-ordernonlinear systems using a single chattering free controlsignal, with good transient and steady state perfor-mances despite all the aforementioned perturbations.In order to demonstrate these results, numerical simu-lations are performed for cases where a Lur’e like sys-tem is synchronized with a Chua’s circuit, and whereit is controlled to track a given trajectory.

aInstitute of Smart Systems Technologies, Alpen-Adria Univer-sitat, Klagenfurt, [email protected]

Harvesting energy from fat-tail randomvibrations: an incomplete electronicanalogy

J.I. Pena Rosselloa, M.G. dell’Erbaa, R.R. Dezaa,J.I. Dezab and H.S. Wioc

In recent work [1], we have found strong evidencethat nonlinear “springs” with square well-like dynam-ics are more efficient for piezoelectric energy harvest-ing from random vibrations the “fatter” their tail be-comes, because they better profit from the large andstrongly self-correlated excursions of the environmen-tal vibration process. We considered a 1D anharmonicoscillator mediating between a source of mechanical vi-brations and a piezoelectric transducer, whose voltageV (t) = Kcx(t) is fed onto a load circuit with resis-tance R and capacitance τp/R. The oscillator (massm, damping constant γ) undergoes the transducer’sback-reaction KvV (t), and its autonomous dynamics isgoverned by U(x). The source of mechanical vibrations(to which it is coupled with strength σ) is regarded asstochastic, producing a strongly colored instantaneousforce η(t). The system is thus described by

mx = −U ′(x)− γx−KvV + ση(t), V = Kcx−1

τpV.

Being V 2(t)/R the instantaneous power delivered tothe load resistance, the measure of performance is Vrms

during the observation interval. We have chosen a po-tential of the form

U(x) = −V0/1 + exp [(|x| −R)/a]

(left frame in Fig. 1) [2], which for a → 0 becomesa square well of depth V0 and width 2R, whereas forR >> a and |x| > a resembles a harmonic potential.

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It thus allows us to monitor the deviation from the lin-ear case by just varying parameter a, whereas avoidingunreal infinite walls as it occurs with polynomial po-tentials [3].

Fig. 1: Left: Woods-Saxon potential for V0 = 2 and R = 1;

right: pdf of the Tsallis noise.

As the source of mechanical vibrations we have cho-sen the Tsallis noise η(t) [4], which is dynamically gen-erated by

η = −1

τ

d

dηVq(η) +

1

τξ(t),

with Vq(η) =1

τ(q − 1)ln

[1 + τ(q − 1)

η2

2

],

and ξ(t) is Gaussian, centered, of variance 1 and white,namely 〈ξ(t)ξ(t′)〉 = 2δ(t − t′). For q = 1, η(t) is anOrnstein-Uhlenbeck process with self-correlation timeτ . For q > 3, its pdf is not normalizable. For 1 < q <5/3, η(t) is a supra-Gaussian process, and for q < 1,its pdf has compact support (right frame in Fig. 1).Our focus here are the supra-Gaussian (1 < q < 5/3)and Levy-like (5/3 < q < 3) regimes; namely fat-taildistributions, which are commonly found in nature.

Fig. 2: Efficiency as a function of q, for 1 ≤ q ≤ 3

(supra-Gaussian and Levy-like regimes).

Through Heun integration of the framed equationshere we show that in fact, the efficiency of the energyharvesting process - the power ratio between V 2(t) (de-livered by the system to a unit load resistance) and ηx(delivered by the noise to the system) - grows mono-tonically as a function of q, up to its maximum valueq = 3 (Fig. 2). These results spectacularly confirm ourhypothesis. Moreover, in order to vividly illustrate themechanism taking place, we have fed (through the au-dio output of a computer and using MATLAB’s sound

functions) a Zener diode, as a metaphor of a squarewell. The circuit is shown in panel 3(a), whereas thesuccession of scope captures in panels 3(b)-(d) illus-trates how as q increases, surpassing the dashed linebecomes more probable.

Fig. 3: (a) Circuit of the electronic analogy; (b,c and d) scope

captures for q = 1.0, q = 1.3, and q = 1.6 respectively.

[1] J.I. Deza, R.R. Deza and H.S. Wio, “Wide-spectrum energyharvesting out of colored Levy-like fluctuations, by monos-table piezoelectric transducers”, Europhys. Lett. 100, 38001(2012).

[2] A. Bohr and B.R. Mottelson, Nuclear structure, v.1 (Ben-jamin, New York, 1975).

[3] L. Gammaitoni, I. Neri and H. Vocca, “The benefits of noiseand nonlinearity: Extracting energy from random vibra-tions”, Chem. Phys. Lett. 375, 435 (2010).

[4] H.S. Wio and R.R. Deza, “Noise-induced phenomena: Ef-fects of noises based on Tsallis statistics”, in Bounded noisesin Physics, Biology and Engineering, A. D’Onofrio, ed.(Birkhauser, Basel, 2013).

aIFIMAR (UNMdP-CONICET), Mar del Plata, Argentina;bDONLL (UPC), Terrassa, Spain; cIFCA (UC-CSIC), San-tander, [email protected]

Stochastic-resonant spatiotemporalpatterns in an inhibitorily coupledFitzHugh-Nagumo ring

A.D. Sancheza, G.G. Izusa, M.G. dell’Erbaa, G.A.Zarzaa, N. Martıneza, L. Vassalloa, R.R. Dezaa, G.V.Savinob and C.M. Formiglib

We study the stochastic-resonant synchronizationproperties of a ring of excitable FitzHugh–Nagumocells, when nearest-neighbor units are coupled diffu-sively with strength E through their inhibitor fields.The system is submitted to a common subthreshold adi-abatic signal S(t) = A0 sin Ωt, and independent Gaus-sian white noises with common variance η:

ui = b ui(1− u2i )− vi + r1 ξ(u)i (t) + r2 ξ

(v)i (t) +A0 sin Ωt,

vi = ε (β ui − vi + C) + r3 ξ(u)i (t) + r4 ξ

(v)i (t)

+E [(vi+1 − vi) + (vi−1 − vi)],

with i = 1, . . . , N , uN+1 ≡ u1 and u0 ≡ uN . Theparameters (some of them dictated by consistency) areE = 0.5, A0 = 0.011, Ω = 0.002, ε = 0.01, b = 0.01,β = 0.035, C = 0.02, r1 = cos 0.05, r2 = sin 0.05, r3 =

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ε r1, r4 = ε r2. The germ of the numerically observedstochastic-resonant spatiotemporal self-organization ofthe excitation activity, is captured in a two-cell modelfor which both analytical [1] and experimental results(on an electronic analogue [2]) are discussed. Figures1 and 2 depict respectively the electronic analogue ofthe two-cell model and an oscilloscope capture show-ing the (stochastic-resonant) noise-induced alternancebetween activation patterns.

Fig. 1: Electronic analogue of the two-cell model.

Fig. 2: Oscilloscope capture showing the (stochastic-resonant)

noise-induced alternance between activation patterns.

[1] A.D. Sanchez, G.G. Izus, M.G. dell’Erba and R.R. Deza,“A reduced gradient description of stochastic-resonant spa-tiotemporal patterns in a FitzHugh–Nagumo ring with elec-tric inhibitory coupling”, Phys. Lett. A 378, 1579–1583(2014).

[2] G.V. Savino and C.M. Formigli, “Nonlinear electronic circuitwith neuron like bursting and spiking dynamics”, BioSys-tems 97, 9–14 (2009).

aIFIMAR (UNMdP-CONICET), Mar del Plata, Argentina;bFCyT-UNT, San Miguel de Tucuman, [email protected]

Automatic melody generation consider-ing motif using genetic algorithm

Masakazu Sanpeia and Yuko Osanaa

Since the first approach to the automatic composi-tion in 1957, a lot of methods for the automatic compo-sition have been proposed. In this research, we proposean automatic melody generation considering motif us-ing genetic algorithm [1]. In the proposed automaticmelody generation system, sample melody is dividedinto some motifs, and rhythm sequences of all motifsare generated randomly considering rhythm features ofthe sample melody. And then, the melodies are gener-ated to the rhythm sequences by genetic algorithms.

In the proposed system, the sample melody is di-vided into some motifs, and the new melodies aregenerated considering motifs. In this system, first,rhythm sequences of all motifs are generated consid-ering rhythm features of sample melody. And then,some melodies are generated to the rhythm sequencesby genetic algorithm. In this system, the number cor-responding to tone candidates for each sound in basicmotifs and derivation motif generation rules are ex-pressed as genes. In the proposed system, the fitnessof the gene for each melody is calculated based on (1)sequences of non-harmonic tones, (2) distribution ofdifference between two tones, (3) sequences of leaps,(4) derived notes and (5) last tone.

Figure 1 shows an example of generated melody bythe proposed system. In this figure, A0 and so on showthe beginning of motif. Figure 2 shows a transitionof fitness. Figure 3 shows the distribution of differ-ence between two tones. As shown in this figure, thedistribution of difference between two tones of initialindividuals is not similar to that in the sample melody.In contrast, the distribution of difference between twotones in the 100th generation is similar to that in thesample melody.

Fig. 1: Example of generated melody.

[1] D.E. Goldberg: Genetic Algorithms in Search, Optimization,and Machine Learning, Addison-Wesley Longman Publish-ing, 1989.


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Fig. 2: Transition of fitness.

Fig. 3: Distribution of difference between two tones.

Booklet composed by T. Lorimer and F. Gomez.

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abstract booklet - msu.ru · 2015. 9. 13. · plamen ch. ivanov physics department, boston...

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