Identification of the nonlinear state-space dynamics of the action-perception cycle for visually induced postural sway

Abstract

Human subjects standing in a sinusoidally moving visual environment display postural sway with characteristic dynamical properties. We analyzed the spatiotemporal properties of this sway in an experiment in which the frequency of the visual motion was varied. We found a constant gain near 1, which implies that the sway motion matches the spatial parameters of the visual motion for a large range of frequencies. A linear dynamical model with constant parameters was compared quantitatively with the data. Its failure to describe correctly the spatiotemporal properties of the system led us to consider adaptive and nonlinear models. To differentiate between possible alternative structures we directly fitted nonlinear differential equations to the sway and visual motion trajectories on a trial-by-trial basis. We found that the eigenfrequency of the fitted model adapts strongly to the visual motion frequency. The damping coefficient decreases with increasing frequency. This indicates that the system destabilizes its postural state in the inertial frame. This leads to a faster internal dynamics which is capable of synchronizing posture with fast-moving visual environments. Using an algorithm which allows the identification of essentially nonlinear terms of the dynamics we found small nonlinear contributions. These nonlinearities are not consistent with a limit-cycle dynamics, accounting for the robustness of the amplitude of postural sway against frequency variations. We interpret our results in terms of active generation of postural sway specified by sensory information. We derive also a number of conclusions for a behavior-oriented analysis of the postural system.