Nonequilibrium Phase Transitions in Coordinated Movements Involving Many Degrees of Freedom a

The movements of animals and people are ordered spatiotemporal structures even though they arise from microscopic sources (e.g. neuronal, skeletomuscular, vascular) of huge dimensionality. How are such ordered states to be understood? The interdisciplinary field of synergetics' offers a means by which the behavior of very high dimensional systems may be described in terms of a few macroscopic quantities called order parameters. In coordinated biological motion the phase relation (4) among interacting components may be a relevant order parameter characterizing different modes of coordination. In experiments on oscillatory human hand rn~vements ,~ abrupt transitions between one mode of coordination (4 = 180 deg) and another (4 = 0 deg) were observed as a control parameter (pacing frequency) was scaled beyond a critical value (FIG. 1). This phenomenon (analogous, perhaps, to locomotory gait changes, e.g.