Abstract
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 the necessary and sufficient condition of the asymptotic stability in views of probability one 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 brain. The effect of the strength of noise on the human quiet standing losing stability is weak for a small delay. With the delay increasing, such 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.
Highlights
The human quiet standing model is complex neuromuscular control biological system with time delay
We use a simplified single inverted pendulum model for the human in quiet standing with stochastic perturbation 6, 8, 16 : Iθγθ − mgL sin θ f θ t − τ cη t θ t, 2.1 where I represents the moment of inertia of human body around the ankle, θ the tilt angle, g the gravity acceleration, m the body mass, L the distance from the ankle joint to the body COM Center of Mass, γ the damping coefficient, f x t the postural sway feedback function, τ the time delay, and η t a stochastic process of zero mean value Gauss white noise
We reduce the system to a two-dimensional ordinary differential equation 3.20
Summary
The human quiet standing model is complex neuromuscular control biological system with time delay. Most of researches about the time-delay human standing model still with stochastic perturbation are studied by numerical simulation. Influence of delay and noise on the Hopf bifurcation and asymptotic stability will be analyzed theoretically It becomes infinite-dimensional problem due to considering the time delay in quiet standing system, which increases work difficulty. The asymptotic Lyapunov stability with probability one for quasi-integrable and nonresonant Hamiltonian systems with time-delayed feedback control has been studied in terms of the stochastic average method. Asymptotic techniques, such as Taylor series expansion, integral averaging method, Fourier series, and perturbation methods, are often used under the assumption of small delays.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
