Chaotic Frequency Scaling in a Coupled Oscillator Model for Free Rhythmic Actions

Abstract

The question of how best to model rhythmic movements at self-selected amplitude-frequency combinations, and their variability, is a long-standing issue. This study presents a systematic analysis of a coupled oscillator system that has successfully accounted for the experimental result that humans' preferred oscillation frequencies closely correspond to the linear resonance frequencies of the biomechanical limb systems, a phenomenon known as resonance tuning or frequency scaling. The dynamics of the coupled oscillator model is explored by numerical integration in different areas of its parameter space, where a period doubling route to chaotic dynamics is discovered. It is shown that even in the regions of the parameter space with chaotic solutions, the model still effectively scales to the biomechanical oscillator's natural frequency. Hence, there is a solution providing for frequency scaling in the presence of chaotic variability. The implications of these results for interpreting variability as fundamentally stochastic or chaotic are discussed.