Effects of time delay and noise on asymptotic stability in human quiet standing model (Q613853)

Summary: A human quiet standing stability is discussed in this paper. The model under consideration is proposed to be a delayed differential equation (DDE) with multiplicative white noise perturbation. The method of the center manifold is generalized to reduce a delayed differential equation to a two-dimensional ordinary differential equation to study delay-induced instability or Hopf bifurcation. Then, the stochastic average method is employed to obtain the Itô equation. Thus, the top Lyapunov exponent is calculated and a necessary and sufficient condition for the almost sure asymptotic stability is obtained. The results show that the exponent is related to not only the strength of noise but also the delay, namely, the reaction speed of the brain. The effect of the strength of noise on the human quiet standing losing stability is weak for a small delay. With increasing delay, this effect becomes stronger and stronger. A small change in the strength of noise may destabilize the quiet standing for a large delay. It implies that a person with slow reaction is easy to lose the stability of his/her quiet standing.