Extending the HKB model of coordinated movement to oscillators with different eigenfrequencies

We study the dynamics of a system of coupled nonlinear oscillators that has been used to model coordinated human movement behavior. In contrast to earlier work we examine the case where the two component oscillators have different eigenfrequencies. Problems related to the decomposition of a time series (from an experiment) into amplitude and phase are discussed. We show that oscillations at multiples of the main frequency of the oscillator system may occur in the phase and amplitude due to the choice of a coordinate system and how these oscillations can be eliminated. We derive an explicit equation for the dynamics of the relative phase of the oscillator system in phase space that enables a direct comparison between theory and experiment.

[1]  E.,et al.  THE SPACE-TIME BEHAVIOR OF SINGLE AND BIMANUAL RHYTHMICAL MOVEMENTS : DATA AND MODEL * , 2022 .

[2]  E. Saltzman,et al.  Space-time behavior of single and bimanual rhythmical movements: data and limit cycle model. , 1987 .

[3]  M. Turvey,et al.  Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people. , 1990, Journal of experimental psychology. Human perception and performance.

[4]  K. Steinmüller.  HAKEN, H.: Synergetics. An Introduction. Springer‐Verlag, Berlin‐Heidelberg‐New York 1977. XII, 325 S., 125 Abb., DM 72.—. , 1978 .

[5]  M. Turvey,et al.  Coupling dynamics in interlimb coordination. , 1993, Journal of experimental psychology. Human perception and performance.

[6]  J. Kelso,et al.  Action-Perception as a Pattern Formation Process , 2018, Attention and Performance XIII.

[7]  J. A. S. Kelso,et al.  Cooperative Phenomena in Biological Motion , 1985 .

[8]  J. Kelso,et al.  Manipulating symmetry in the coordination dynamics of human movement. , 1995, Journal of experimental psychology. Human perception and performance.

[9]  J. Kelso,et al.  Posturally induced transitions in rhythmic multijoint limb movements , 2004, Experimental Brain Research.

[10]  J. Kelso.  Phase transitions and critical behavior in human bimanual coordination. , 1984, The American journal of physiology.

[11]  Professor Dr. Dr. h.c. Hermann Haken,et al.  Synergetic Computers and Cognition , 1991, Springer Series in Synergetics.

[12]  J. Kelso,et al.  A quantitative approach to understanding the formation and change of coordinated movement patterns. , 1989, Journal of motor behavior.

[13]  N. Bogolyubov,et al.  Asymptotic Methods in the Theory of Nonlinear Oscillations , 1961 .

[14]  H. Haken,et al.  Phase-locked modes, phase transitions and component oscillators in biological motion , 1987 .

[15]  Michael T. Turvey,et al.  Phase-entrainment dynamics of visually coupled rhythmic movements , 1994, Biological Cybernetics.

[16]  P J Beek,et al.  Dynamical substructure of coordinated rhythmic movements. , 1991, Journal of experimental psychology. Human perception and performance.

[17]  H. Haken,et al.  A theoretical model of phase transitions in human hand movements , 2004, Biological Cybernetics.

[18]  J. Kelso,et al.  Symmetry breaking dynamics of human multilimb coordination. , 1992, Journal of experimental psychology. Human perception and performance.