Delayed stochastic differential model for quiet standing.

A physiological quiet standing model, described by a delayed differential equation, subject to a white noise perturbation, is proposed to study the postural control system of human beings. It has been found that the white noise destabilizes the equilibrium state, and inertia accelerates the destabilizing process, and that the position of a person is detected and processed by the person's nervous system with a delay. This paper focuses on the analysis of Hopf bifurcation and its stability in this context. Based on the analytical predictions confirmed by numerical simulations, it has been shown that the posture of a person is controlled in such a way that possible amplitude oscillations are minimized.