Abstract
The order parameter equation for the relative phase of correlated hand movements, derived in a previous paper by Haken et al. (1985), is extended to a time-dependent stochastic differential equation. Its solutions are determined close to stationary points and for the transition region. Remarkably good agreement between this theory and recent experiments done by Kelso and Scholz (1985) is found, and new predictions are offered.
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References
Ames WF (1977) Numerical methods for partial differential equations. Academic Press, New York
Broggi G, Lugiato LA (1984) Transient noise-induced optical bistability. Phys Rev A29:2949
Gardiner CW (1983) Handbook of stochastic methods for physics, chemistry, and the natural sciences. Springer series in synergetics, vol. 13. Springer, Berlin Heidelberg New York
Haken H (1975) Cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems. Rev Mod Phys 47:67–121
Haken H (1983) Synergetics: an introduction. Nonequilibrium phase transitions and self-organization in physics, chemistry, and biology. 3rd edn. Springer, Berlin Heidelberg New York
Haken H, Kelso JAS, Bunz H (1985) A theoretical model of phase transitions in human hand movements. Biol Cybern 51:347–356
Kelso JAS (1981) On the oscillatory basis of movement. Bull Psychon Soc 18:63
Kelso JAS (1984) Phase transitions and critical behavior in human bimanual coordination. Am J Phys: Reg Integr Comp 15:R1000-R1004
Kelso JAS, Scholz J (1985) Cooperative phenomena in biological motion. In: Haken H (ed) Complex systems-operational approaches in neurobiology, physical systems and computers. Springer, Berlin Heidelberg New York, pp 124–149
Kelso JAS, Tuller B (1985) Intrinsic time in speech production: Theory, methodology, and preliminary observations. Hask Lab Stat Rpt Sp Res SR-81:23–39. To appear in: Keller E, Gopnik M (eds) Sensory and motor processes in language. Erlbaum (in press) Hillsdale, NJ
Kelso JAS, Southard D, Goodman D (1979) On the nature of human interlimb coordination. Science 203:1029–1031
Kelso JAS, Tuller B, Harris KS (1981) A “dynamic pattern” perspective on the control and coordination of movement. Hask Lab Stat Rpt Sp Res SR-65:157–196. Also published in: MacNeilage P (ed) (1983) The production of speech. Springer, Berlin Heidelberg New York
Kugler PN, Kelso JAS, Turvey MT (1980) Coordinative structures as dissipative structures. I. Theoretical lines of convergence. In: Stelmach GE, Requin J (eds) Tutorials in motor behavior. North-Holland, Amsterdam
Schmidt RA (1982) Motor control and learning: a behavioral emphasis. Champaign, IL, Human Kinetics
Sleigh MA, Barlow DI (1980) Metachronism and control of locomotion in animals with many propulsive structures. In: Elder HY, Trueman ET (eds) Aspects of animal locomotion. Cambridge University Press, Cambridge
Turvey MT (1977) Preliminaries to a theory of action with reference to vision. In: Shaw R, Bransford J (eds) Perceiving, acting and knowing: toward an ecological psychology. Erlbaum Hillsdale, NJ
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Schöner, G., Haken, H. & Kelso, J.A.S. A stochastic theory of phase transitions in human hand movement. Biol. Cybern. 53, 247–257 (1986). https://doi.org/10.1007/BF00336995
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DOI: https://doi.org/10.1007/BF00336995