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Thoughts on movement generation…

Thoughts on movement generation…. Viktor Jirsa. position x. velocity y. position x. nullclines. Phenomena – phenomenological modeling I. position x. time. False starts. position x. velocity y. position x. Phenomena – phenomenological modeling II. nullclines. separatrix.

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Thoughts on movement generation…

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  1. Thoughts on movement generation… Viktor Jirsa

  2. position x velocity y position x nullclines Phenomena – phenomenological modeling I

  3. position x time False starts

  4. position x velocity y position x Phenomena – phenomenological modeling II nullclines separatrix

  5. position x velocity y position x nullclines topological constraints on 2-dim. dynamics separatrix Phenomena – phenomenological modeling III

  6. position x velocity y position x Mathematical representation Task constraints nullclines separatrix

  7. Task conditions monostable rhythmic bistable task conditions define topology in phase space by controling the shape of the nullclines

  8. fixed points Excitator Schöner (1990) Jirsa et al. (1999) Beek et al. (2001) Sternad et al. (2001) Jirsa & Kelso (2003) …

  9. Bifurcation diagram

  10. Transforms to experimental space

  11. Bistable Excitator

  12. Bistable excitator overshoot experiment theory overshoot: - slow dynamics - refractory Co-existence of fixed points?

  13. Monostable Excitator

  14. Rhythmic Excitator

  15. Coupled Excitators: discrete movement coupling: - sigmoidal - HKB (truncated sigmoidal)

  16. Euclidean distance in phase space

  17. Haken, Kelso, Bunz 1984 Coupled Excitators: rhythmic paradigm

  18. acceleration (convergence) Coupled Excitators: discrete movement

  19. deceleration (divergence) acceleration (convergence) Coupled Excitators: discrete movement crucial parameter: distance of the two effectors

  20. Time difference Acceleration/deceleration time = 50ms

  21. Dagmar’s discrete-rhythmic interaction

  22. … two trials

  23. Dagmar’s for many trials….

  24. Phase picture for many trials

  25. 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)

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