1. Thoughts on movement generation… Viktor Jirsa

2. Center for Complex Systems & Brain Sciences, Physics Dept. Phenomena – phenomenological modeling I position x velocity y nullclines

3. Center for Complex Systems & Brain Sciences, Physics Dept. False starts time position x

4. Center for Complex Systems & Brain Sciences, Physics Dept. Phenomena – phenomenological modeling II position x velocity y separatrix nullclines

5. Center for Complex Systems & Brain Sciences, Physics Dept. Phenomena – phenomenological modeling III position x velocity y separatrix nullclines topological constraints on 2-dim. dynamics

6. Center for Complex Systems & Brain Sciences, Physics Dept. Task constraints Mathematical representation position x velocity y separatrix nullclines

7. Center for Complex Systems & Brain Sciences, Physics Dept. Task conditions task conditions define topology in phase space by controling the shape of the nullclines monostable bistable rhythmic

8. Center for Complex Systems & Brain Sciences, Physics Dept. Excitator fixed points Schöner (1990) Jirsa et al. (1999) Beek et al. (2001) Sternad et al. (2001) Jirsa & Kelso (2003) …

9. Center for Complex Systems & Brain Sciences, Physics Dept. Bifurcation diagram

10. Center for Complex Systems & Brain Sciences, Physics Dept. Transforms to experimental space

11. Center for Complex Systems & Brain Sciences, Physics Dept. Bistable Excitator

12. Center for Complex Systems & Brain Sciences, Physics Dept. Bistable excitator experimenttheory overshoot overshoot: - slow dynamics - refractory Co-existence of fixed points?

13. Center for Complex Systems & Brain Sciences, Physics Dept. Monostable Excitator

14. Center for Complex Systems & Brain Sciences, Physics Dept. Rhythmic Excitator

15. Center for Complex Systems & Brain Sciences, Physics Dept. Coupled Excitators: discrete movement coupling: - sigmoidal - HKB (truncated sigmoidal)

16. Center for Complex Systems & Brain Sciences, Physics Dept. Euclidean distance in phase space

17. Center for Complex Systems & Brain Sciences, Physics Dept. Coupled Excitators: rhythmic paradigm Haken, Kelso, Bunz 1984

18. Center for Complex Systems & Brain Sciences, Physics Dept. acceleration (convergence) Coupled Excitators: discrete movement

19. Center for Complex Systems & Brain Sciences, Physics Dept. acceleration (convergence) Coupled Excitators: discrete movement deceleration (divergence) crucial parameter: distance of the two effectors

20. Center for Complex Systems & Brain Sciences, Physics Dept. Time difference Acceleration/deceleration time = 50ms

21. Center for Complex Systems & Brain Sciences, Physics Dept. Dagmars discrete-rhythmic interaction

22. Center for Complex Systems & Brain Sciences, Physics Dept. … two trials

23. Center for Complex Systems & Brain Sciences, Physics Dept. Dagmars for many trials….

24. Center for Complex Systems & Brain Sciences, Physics Dept. Phase picture for many trials

25. Center for Complex Systems & Brain Sciences, Physics Dept. Key points topology in phase space constrains dynamics system (fixed points, refractory regimes, …) but: specific mathematical realizations not unique task conditions define topology of flow in phase space threshold (separatrix) makes false starts possible coupling causes convergence/divergence (special case: rhythmic bimanual coordination)

26. Center for Complex Systems & Brain Sciences, Physics Dept.