Stability and the maintenance of balance following a perturbation from quiet stance

We investigate stability and the maintenance of balance with the use of tools from dynamical systems. In particular we investigate the application of such tools to the study of the ground reaction forces resulting from an athlete being perturbed from quiet stance. We develop a nonlinear model consisting of a set of coupled vector fields for the derivative with respect to time of the angles between the resultant ground reaction forces and the vertical in the anteroposterior and mediolateral directions. This model contains a basin of attraction bound by a closed curve which we call the critical curve. It is only inside this curve that perturbations can be corrected, with the orbit spiraling onto an attractor corresponding to quiet stance. We show how the critical curve and also the strength of the attractor found in the basin of attraction can be fit to model the experimental data (time series) for an individual athlete. We also discuss how our model can be used to identify nonsymmetric behavior caused by muscle imbalances and differences in the ranges of motion on either side of the body.