what is simulation ?
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What is simulation ?. "... conceive simulation as a special case of a more general and conceptually richer paradigm of model-based activities ..“ (Ören 1984) - PowerPoint PPT PresentationTRANSCRIPT
What is simulation ?
"... conceive simulation as a special case of a more general and conceptually richer paradigm of model-based activities ..“ (Ören
1984)
"Simulation is the process of designing a model of a real system and conducting experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various
strategies ... for the operation of the system“
(Shannon 1975)
Work definitionsMODEL:
A model is a goal oriented representation of a system that exists in reality or can be realized
Symbolic Language
Real World
Model
(Theory )
objects
Interpretations
Work definitions
Computermodel:A computer model = an algorithm = of a system
that can be realized in the real world
Simulation:Simulation is stepping through a computer
model with the purpose to describe the behavior of a real system
Paradigms Programs of Research
"A scientific view on the world guided by a methodology .... disciplinary matrix ... symbolic generalization .. shared
commitment in a particular model"(Kuhn 1970, 1977)
"The history of science has been and should be a history of
completing research programs (or if you wish paradigm's ), but it has not been and must become a succession of periods of normal
science: the sooner competition starts, the better for progress. Theoretical pluralism is better then theoretical monism"
(Lakatos 1970)
A successful research program is one that generates a series of theories (a problem shift) which consistently is theoretically
progressive and intermittently is empirically progressive. Mature science consists of research programs, whereas immature science
consist of a "mere patched up pattern of trial and error"(Lakatos 1970)
Paradigms of Simulation
• Discrete opposite Continue
• Stochastic opposite Deterministic
* Recursive causality
opposite
NON recursive causality
* Linear opposite Non linear
View on Causality
Non RecursiveOneway Traffic Cause Effect
Reichenbach, Popper, traditional view in Methodological TextbooksAnd view of most SEM modelers
+ Linear dependency
Effect = constant*CausePearson-correlationLineair regression
Path models
AB
C
E F+ +
+
+
++
View on Causality
RecursiveCircle between Cause and Effect
Cause Effect
t
View on Causality System Dynamics
• Feedback loop
Cause Effect
Goal
t
View on Causality System Dynamics
Feedback (Wiener, Forrester)
Goal searching systemInteraction between variables
Behavior
Norms
DBehavior
View on Causality System Dynamics
A(t) B(t+t)A(t+2t)
t
Mathematical viewed it leads to a:Recursive Difference equation
D A/ D t = F(A, t)
Modeling Recursive CausalitySYSTEMDYNAMICS
Holistic approach, feedback(Forester, Meadows)
&From Verbal Description
toMathematical models of Causality
(Blalock)
+SOFTWARE STELLA
(Meadows, Richmond)
UserfriendlyModeling of Causality
By means of Graphic Symbols
Approach Stella FROM VERBAL DESCRIPTION
VIACAUSAL DIAGRAMs
ANDFEEDBACK DESCRIPTIONS
VIA
FLOW DIAGRAMS
TO
DIFFERENTIAL EQUATIONS that are
OPERATIONAL COMPUTERMODELS
STELLA
A Demonstration
From Verbal Description to
Causal Diagrams
An Example
Verbal Description:
Money put on the bank produces after some time interest, that result in more
capital on the bank, producing after another period of time -supposing a
fixed rate of interest- more interest, and as a consequence more capital, and so
on.
From Verbal Description to
Causal Diagrams
Causal Diagram
+
+
++
Capital
Interest
Rate of interest
Another example
Causal diagram
-
+
+ +
Verbal Description? An Exercise
Number of population
Number of deaths Newborns
BirthrateDeath rate
Verbal Description:
The number of the newborns and the number of deaths are proportional to the number of the population. The
number of newborns is proportional to the birthrate. The number of deaths is
proportional to the deathrate. Newborns add up the population. The number of death subtracts from the population
(alternative statements are possible)
CAUSAL DESCRIPTIONSCausal diagram
A
B C
-
+
+ +
D E
++
CAUSALE DESCRIPTIONS Causal Matrix
Cause A B C D E
A - +
B + +
C + +
D
E
Effect
STELLA
• AN EXERCISE
– GROWTH OF CAPITAL
FROM CAUSAL DIAGRAMS AND FEEDBACK DESCRIPTIONS
VIA A FLOWDIAGRAM
Capital
Interest
RateofInterest
To a DIFFERENCE EQUATION
Capital*restRateofInteyearTime
Capital
FROM CAUSAL DIAGRAMS AND FEEDBACK DESCRIPTIONS
VIA a FLOW DIAGRAM
FROM CAUSAL DIAGRAMS AND FEEDBACK DESCRIPTIONS
VIA a FLOW DIAGRAM
and a DIFFERENCE EQUATION
To a DIFFERENTIAL EQUATION (t 0)
IN STELLA NOTATIONCapital(t) = Capital(t - dt) + (Interest) * dt
INIT Capital = 1000INFLOWS:
Interest = Capital*RateofInterestRateofInterest = 0.05
Capital*restRateofIntedTime
dCapital
Differential Equations
Linear Differential Equations– An Exercise
– Growth of a Population
Differential Equations
Non Linear Differential Equations– An Exercise
– Limited Growth of a Population
Differential Equations
Non Linear Differential Equations– An Exercise
Spread of a disease
WhyNon Linear Differential Equations
in Social Sciences ?
Behavior
Norms
DBehavior
Behavior of an Individual
Feedback Most of time non linear
WhyNon Linear Differential Equations
in Social Sciences ?
Behavior person A
Norms
Interaction between Individuals
Feedback Most of time non linear
Behavior person B
Differential Equations
Non Linear Differential Equations– An Exercise
Coupled Limited Growth
An example of InteractionGP Patient Communication
A simplified kernel of our ModelHow well do we understand the complaint?
What is the information content of this understanding ?
GPvaluationComplaint
driveGP
RatedriveGP
PatientvaluationComplaint
drivePatient
ratedrivePatient
mpltpPatientToGP
mltplierGPtoPatient
GPvaluationComplaint
driveGP
RatedriveGP
PatientvaluationComplaint
drivePatient
ratedrivePatient
mpltpPatientToGP
mltplierGPtoPatient
19: 48 Tue 25 Sep 2007
0. 00 10. 00 20. 00 30. 00 40. 00
Tim e
1:
1:
1:
0, 00
30, 00
60, 00
1: G Pvaluat ionCom plaint
1 1
1
1
G r aph 1 ( Unt it led)
Limited growth: when the GP has said and ask enough about what is in a biomedical sense going on, he or she will stop
talking and stay on a stable valuation of the complaint
When patients need to understand
19: 48 Tue 25 Sep 2007
0. 00 10. 00 20. 00 30. 00 40. 00
Tim e
1:
1:
1:
0, 00
30, 00
60, 00
1: G Pvaluat ionCom plaint
1 1
1
1
G r aph 1 ( Unt it led)
Limited growth: when the Patient has asked and said enough about what is in a biomedical sense going on,
he or she will stop talking and stay on a stable valuation of the complaint
But those two interact!
20:06 Tue 25 Sep 2007
0.00 10.00 20.00 30.00 40.00
Time
1:
1:
1:
0,00
20,00
40,00
1: GPvaluationComplaint
1
1
1
1
Graph 1 (Untitled)
What happens when a GP has a very strong drive to present his/her message and the patient has a very strong drive to tell
their story?GP drive=Patient drive=2
Unlimited number of outcomes: CHAOS
CHAOSThe logic of It ?
Looking to one side of the coupling
To A plot of outcomes with varying parameter r(of the GPdrive in our case; in this case a normalized graph and r as
transformed parameter)
Coupled Growers
population1
growth1
population 2
growth parameter1
growth 2
growth parameter 2
couplingf actor
Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1
Coupling factor = 0.1
Population1
Population2
5:05 PM Wed, Aug 13, 2008
0.00 10.00 20.00 30.00 40.00
Time
1:
1:
1:
0.00
1.00
2.00
1: population1
1
1
1
1
population1: p1 (Unti tled)
3:12 PM Tue, Aug 19, 2008
0.00 10.00 20.00 30.00 40.00
Time
1:
1:
1:
0.00
1.00
2.00
1: population 2
1
1
1
1
population2 (Unti tled)
Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1
Coupling factor = 0.3
Population1
Population2
5:05 PM Wed, Aug 13, 2008
0.00 10.00 20.00 30.00 40.00
Time
1:
1:
1:
0.00
1.00
2.00
1: population1
1
1
1
1
population1: p1 (Unti tled)
3:13 PM Tue, Aug 19, 2008
0.00 10.00 20.00 30.00 40.00
Time
1:
1:
1:
0.00
1.00
2.00
1: population 2
1
1
1
1
population2 (Unti tled)
Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1
Coupling factor = 0.5
Population1
Population2
2:53 PM Tue, Aug 19, 2008
0.00 10.00 20.00 30.00 40.00
Time
1:
1:
1:
0.00
1.00
2.00
1: population 2
1
1 1
1
population2 (Unti tled)
5:05 PM Wed, Aug 13, 2008
0.00 10.00 20.00 30.00 40.00
Time
1:
1:
1:
0.00
1.00
2.00
1: population1
1
1
1
1
population1: p1 (Unti tled)
Coupled Growersgrowth Parameter 1= 3; growth Parameter 2 = 1
Coupling factor = 1
Population1
Population2
2:54 PM Tue, Aug 19, 2008
0.00 10.00 20.00 30.00 40.00
Time
1:
1:
1:
0.00
1.00
2.00
1: population 2
1
11
1
population2 (Unti tled)
5:05 PM Wed, Aug 13, 2008
0.00 10.00 20.00 30.00 40.00
Time
1:
1:
1:
0.00
1.00
2.00
1: population1
1
1
1
1
population1: p1 (Unti tled)
Coupled GrowersEffects
Plot of changing coupling factorAnd output population1 and 2 ?!
For this STELLA is not suitedUSE MATLAB
MATLAB
• Some Experiments with Coupled Growers•
X n+1 = F(Xn;αX)+ε[F(Yn;αY )−F(Xn;αX),Y n+1 = F(Yn;αY )− ε[F(Yn;αY)−F(Xn;αX)].
Experiments with Coupled Growers(Savi 2007)
X n+1 = F(Xn;αX)+ε[F(Yn;αY )−F(Xn;αX),Y n+1 = F(Yn;αY )− ε[F(Yn;αY)−F(Xn;αX)].
Logistic map bifurcation diagram αX = 3.8 (chaos) and αY=2.5 (period 1)
ε
X n+1
Experiments with Coupled Growers(Savi 2007)
X n+1 = F(Xn;αX)+ε[F(Yn;αY )−F(Xn;αX),Y n+1 = F(Yn;αY )− ε[F(Yn;αY)−F(Xn;αX)].
Logistic map bifurcation diagram αX = 3.8 (chaos) and αY=2.5 (period 1)
ε
Yn+1
Some Literature
• Barlas, Y. 1989. “Multiple Tests for Validation of System Dynamics Type of Simulation Models.” European Journal of Operational Research 42(1):59-87.
• Dijkum C. van (2001). A Methodology for Conducting Interdisciplinary Social Research. European Journal of Operational Research,Vol.128,Iss. 2, 290-299.
• Dijkum C. van, Landsheer H. (2000). Experimenting with a Non-linear Dynamic Model of Juvenile Criminal Behavior. Simulation & Gaming, Vol.31, No.4, 479-490.
• Dijkum C. , Mens-Verhulst J. van, Kuijk E. van, Lam N. (2002), System Dynamic Experiments with Non-linearity and a Rate of Learning, Journal of Artificial Societies and Social Simulation, Vol. 5, 3.
• Dijkum, C. van, Verheul W. Bensing J., Lam N., Rooi J. de (2008). “Non Linear Models for the Feedback between GP and Patients.” In Cybernetics and Systems. Trappl R. (ed). Vienna: Austrian Society for Cybernetic Studies. (download: http://www.nosmo.nl/rc33/nonlinear.pdf)
• Forrester, J.W. (1968). Principles of Systems. Cambridge MA: Wright-Allen Press.
Some Literature
• Haefner J. W. (1996). Modeling biological systems. New York: Chapman & Hall.
• Hanneman, R.A (1988). Computer-assisted theory building: Modeling dynamic social systems. Newbury Park: Sage.
• Richardson, G.P. and A.L.Pugh III. 1981. Introduction To System Dynamics Modeling With DYNAMO. Portland, OR: Productivity Press.
• Schroots J., Dijkum C. van (2004). Autobiographical Memory Bump- A Dynamic Lifespan Model. Dynamical Psychology: An International, Interdisciplinary Journal of Complex Mental Processes. (http://www.goertzel.org/dynapsyc/dynacon.html)