thoughts on movement generation… viktor jirsa. center for complex systems & brain sciences,...
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Thoughts on movement generation…Thoughts on movement generation…
Viktor Jirsa
Center for Complex Systems & Brain Sciences, Physics Dept.
Phenomena – phenomenological modeling IPhenomena – phenomenological modeling I
position x
pos
itio
n x
velo
city
y
nullclines
),(
),(
yxfy
yxgx
0
0
y
x
Center for Complex Systems & Brain Sciences, Physics Dept.
False startsFalse starts
time
posi
tion
x
Center for Complex Systems & Brain Sciences, Physics Dept.
Phenomena – phenomenological modeling IIPhenomena – phenomenological modeling II
position x
pos
itio
n x
velo
city
y
separatrix
nullclines
Center for Complex Systems & Brain Sciences, Physics Dept.
Phenomena – phenomenological modeling IIIPhenomena – phenomenological modeling III
position x
pos
itio
n x
velo
city
y
separatrix
nullclines
),(
),(
yxfy
yxgx
topological constraints
on 2-dim. dynamics
Center for Complex Systems & Brain Sciences, Physics Dept.
Task constraints
Mathematical representationMathematical representation
position x
pos
itio
n x
velo
city
y
separatrix
nullclines
Center for Complex Systems & Brain Sciences, Physics Dept.
Task conditionsTask conditions
task conditions define topology in phase space by controling the shape of the nullclines
monostablebistablerhythmic
Center for Complex Systems & Brain Sciences, Physics Dept.
ExcitatorExcitator
fixed points
Schöner (1990)Jirsa et al. (1999)Beek et al. (2001)Sternad et al. (2001)Jirsa & Kelso (2003)…
Center for Complex Systems & Brain Sciences, Physics Dept.
Bifurcation diagramBifurcation diagram
Center for Complex Systems & Brain Sciences, Physics Dept.
Transforms to experimental spaceTransforms to experimental space
Center for Complex Systems & Brain Sciences, Physics Dept.
Bistable ExcitatorBistable Excitator
Center for Complex Systems & Brain Sciences, Physics Dept.
Bistable excitatorBistable excitator
experiment theory
overshoot
overshoot: - slow dynamics- refractory
Co-existence of fixed points?
Center for Complex Systems & Brain Sciences, Physics Dept.
Monostable ExcitatorMonostable Excitator
Center for Complex Systems & Brain Sciences, Physics Dept.
Rhythmic ExcitatorRhythmic Excitator
Center for Complex Systems & Brain Sciences, Physics Dept.
Coupled Excitators: discrete movementCoupled Excitators: discrete movement
coupling: - sigmoidal - HKB (truncated sigmoidal)
Center for Complex Systems & Brain Sciences, Physics Dept.
Euclidean distance in phase spaceEuclidean distance in phase space
Center for Complex Systems & Brain Sciences, Physics Dept.
Coupled Excitators: rhythmic paradigmCoupled Excitators: rhythmic paradigm
Haken, Kelso, Bunz 1984
2sin2sin ba
Center for Complex Systems & Brain Sciences, Physics Dept.
acceleration(convergence)
Coupled Excitators: discrete movementCoupled Excitators: discrete movement
Center for Complex Systems & Brain Sciences, Physics Dept.
acceleration(convergence)
Coupled Excitators: discrete movementCoupled Excitators: discrete movement
deceleration(divergence)
crucial parameter:distance of the two effectors
Center for Complex Systems & Brain Sciences, Physics Dept.
Time differenceTime difference
Acceleration/deceleration time = 50ms
Center for Complex Systems & Brain Sciences, Physics Dept.
Dagmar’s discrete-rhythmic interaction Dagmar’s discrete-rhythmic interaction
Center for Complex Systems & Brain Sciences, Physics Dept.
… … two trialstwo trials
Center for Complex Systems & Brain Sciences, Physics Dept.
Dagmar’s for many trials….Dagmar’s for many trials….
Center for Complex Systems & Brain Sciences, Physics Dept.
Phase picture for many trialsPhase picture for many trials
Center for Complex Systems & Brain Sciences, Physics Dept.
Key pointsKey points
topology in phase space constrains dynamics system (fixed points, refractory regimes, …)
but: specific mathematical realizations not uniquetask conditions define topology of flow in phase
spacethreshold (separatrix) makes ‘false starts’ possiblecoupling causes convergence/divergence (special
case: rhythmic bimanual coordination)
Center for Complex Systems & Brain Sciences, Physics Dept.
Center for Complex Systems & Brain Sciences, Physics Dept.