Effects of Time Delay and Noise on Asymptotic Stability in Human Quiet Standing Model
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-10-11
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Wang, Caihong& Xu, Jian. 2010. Effects of Time Delay and Noise on Asymptotic Stability in Human Quiet Standing Model. Mathematical Problems in Engineering،Vol. 2010, no. 2010, pp.1-14.
https://search.emarefa.net/detail/BIM-501490
Modern Language Association (MLA)
Wang, Caihong& Xu, Jian. Effects of Time Delay and Noise on Asymptotic Stability in Human Quiet Standing Model. Mathematical Problems in Engineering No. 2010 (2010), pp.1-14.
https://search.emarefa.net/detail/BIM-501490
American Medical Association (AMA)
Wang, Caihong& Xu, Jian. Effects of Time Delay and Noise on Asymptotic Stability in Human Quiet Standing Model. Mathematical Problems in Engineering. 2010. Vol. 2010, no. 2010, pp.1-14.
https://search.emarefa.net/detail/BIM-501490
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-501490