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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (1): 11-22.doi: https://doi.org/10.1007/s10483-011-1389-7

• Articles • 上一篇    下一篇

Stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise

郑言 黄建华   

  1. Department of Mathematics, National University of Defense Technology, Changsha 410073, P. R. China
  • 收稿日期:2010-08-25 修回日期:2010-11-26 出版日期:2011-01-10 发布日期:2011-01-01

Stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise

ZHENG Yan, HUANG Jian-Hua   

  1. Department of Mathematics, National University of Defense Technology, Changsha 410073, P. R. China
  • Received:2010-08-25 Revised:2010-11-26 Online:2011-01-10 Published:2011-01-01

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摘要： The current paper is devoted to the study of the stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise. First, the dynamics of stochastic FitzHugh-Nagumo systems are studied. Then, the existence and uniqueness of their invariant measures, which mix exponentially are proved. Finally, the asymptotic behaviors of invariant measures when size of noise gets to zero are investigated.

Abstract: The current paper is devoted to the study of the stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise. First, the dynamics of stochastic FitzHugh-Nagumo systems are studied. Then, the existence and uniqueness of their invariant measures, which mix exponentially are proved. Finally, the asymptotic behaviors of invariant measures when size of noise gets to zero are investigated.

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