EXTENDING THE HKB MODEL OF COORDINATED MOVEMENT TO OSCILLATORS WITH DIFFERENT EIGENFREQUENCIES

We study the dynamics of a system of coupled nonlinear oscillators tha t has been used to model coordinated human movement behavior. In contr ast to earlier work we examine the case where the two component oscill ators have different eigenfrequencies. Problems related to the decompo sition of a time series (from an experiment) into amplitude and phase are discussed. We show that oscillations at multiples of the main freq uency of the oscillator system may occur in the phase and amplitude du e 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.