Autonomous and Nonautonomous Dynamics of Coordinated Rhythmic Movements

Recently, accounts of human rhythmic movement have been given in terms of nonlinear dissipative dynamics with special emphasis on the autonomous dynamics that characterize self-organizing systems. In this article, an argument is made for a modeling strategy that allows for and, when possible, attempts to capitalize on the incorporation of nonautonomous dynamics in models of human rhythmic movement, that is, dynamics that characterize systems that are forced externally. The problem is to incorporate these nonautonomous dynamics nonarbitrarily. Cascade juggling and swinging hand-held pendulums provide the coordinated rhythmic movements to which the argument is applied. Empirical and theoretical analyses suggest that the dynamical description of the movements composing these activities may be nonautonomous when the level of analysis is restricted to the motions of the subsystems in isolation; there are small but systematic forcing contributions in addition to the dominant autonomous components. It is suggested, however, that autonomy is restored when the level of analysis is raised from that of the motions to that of the perception-action cycles, so that dynamically based informational terms are included. At this level, forcing is a function of information, not clock time. A strategy for investigating coordinated rhythmic movements is proposed in which (a) the full complement of tools from nonlinear dynamics is put to use, (b) the determination of nonautonomous components follows the evaluation of autonomous components, and (c) informational variables are sought to transform the resultant dynamical description of the coordinated activity to full autonomy.