The detuning factor in the dynamics of interlimb rhythmic coordination.

ABSTRACT

Dynamical models of two coupled biological oscillators interpret the detuning term as an arithmetic difference between the uncoupled frequencies, delta omega = (omega 1-omega 2). This delta omega interpretation of detuning was addressed in four experiments in which human subjects oscillated pendulums in their right and left hands in 11 frequency locking in antiphase (Experiments 1-3) or inphase (Experiment 4). Differences between the uncoupled frequencies were manipulated through differences in the equivalent simple pendulum lengths, and the effects of this manipulation on the detuning of relative phase from pi or O and the standard deviation of relative phase SD phi were measured. In Experiment 1, the same values of omega i were satisfied by several different physical configurations. The experiment confirmed that the detuning term is related strictly to the uncoupled frequencies rather than to other physical characteristics of the oscillators. Experiments 2, 3 and 4 showed, however, that the particular dependency of fixed point drift and SD phi on delta omega depends on the particulars of omega 1 and omega 2. With variations in delta omega brought about by different omega 1 and omega 2 that always formed a constant ratio, fixed point drift related inversely to delta omega, and SD phi varied with delta omega in ways that depended on the magnitude of the constant ratio. These outcomes do not conform to expectations from models of coordination dynamics that interpret detuning as (omega 1-omega 2).