I. Experimental evidence

Most studies examining the stability and change of patterns in biological coordination have fo- cused on identifying generic bifurcation mechanisms in an already active set of components (see Kelso 1994). A less well understood phenomenon is the process by which previously quiescent degrees of freedom (df ) are spontaneously recruited and active df suppressed. To examine such behavior, in part I we study a single limb system composed of three joints (wrist, elbow, and shoul- der) performing the kinematically redundant task of trac- ing a sequence of two-dimensional arcs of monotonically varying curvature, i. Arcs were displayed on a computer screen in a decreasing and increasing i sequence, and subjects rhythmically traced the arcs with the right hand in the sagittal plane at a fixed frequency (1.0 Hz), with motion restricted to flexion-extension of the wrist, elbow, and shoulder. Only a few coordinative patterns among the three joints were stably produced, e.g., in-phase (flexion-extension of one joint coordinated with flexion- extension of another joint) and antiphase (flexion-exten- sion coordinated with extension-flexion). As i was systematically increased and decreased, switching be- tween relative phase patterns was observed around criti- cal curvature values, i # . A serendipitous finding was a strong 2:1 frequency ratio between the shoulder and elbow that occurred across all curvature values for some subjects, regardless of the wrist-elbow relative phase pat- tern. Transitions from 1:1 to 2:1 frequency entrainment and vice versa were also observed. The results indicate that both amplitude modulation and relative phase change are utilized to stabilize the end-e⁄ector trajectory. In part II, a theoretical model is derived from three coupled nonlinear oscillators, in which the relative phases (/) between the components and the relative joint amplitudes (o) are treated as collective variables with arc curvature as a control parameter.