Phase-entrainment dynamics of visually coupled rhythmic movements.

Do interlimb rhythmic coordinations between individuals exhibit the same relations among the same observable quantities as interlimb rhythmic coordination within an individual? The 1:1 frequency locking between the limbs of two people was investigated using a paradigm in which each person oscillated a hand-held pendulum, achieving and maintaining the mutual entrainment through vision. The intended coordination was antiphase, phi = pi, and the difference between the uncoupled eigen-frequencies, delta omega, was manipulated through differences in the lengths of the two pendulums. The mean phase relation and its variance for visually coupled coordinations differing in delta omega were predicted by an order parameter equation developed by Haken et al. (1985) and Schöner et al. (1986) for the relative phase of correlated movements of limb segments. Specifically, the experiment revealed that: (1) the deviation of phi from pi increased with increasing deviation of delta omega from 0; and (2) fluctuations in phi increased with increasing deviation of delta omega from 0. With deviations of delta omega from 0, new peaks were added at higher harmonics in phi's power spectrum. These results were in agreement with previous research on the stable states of interlimb coordination within a person, mediated by mechanoreceptive rather than photoreceptive mechanisms. Additionally, they were in agreement with previous research on phase transitions in interlimb coordination which have been shown to conform to the same order parameter dynamics whether the coupling be mechanoreceptively or photoreceptively based. It was suggested that phase entrainment in biological movement systems may abide by dynamical principles that are indifferent to the details of the coupling.