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

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Abstract

The current paper is devoted to the study of stochastic stability of FitzHugh-Nagumo systems in infinite lattice perturbed by Gaussian white noise. We first study the dynamics of stochastic FitzHugh-Nagumo systems, then prove the existence and uniqueness of their equilibriums, which mix exponentially. Finally, we investigate asymptotic behavior of equilibriums when the size of noise gets to zero.

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Authors and Affiliations

  1. Department of Mathematics, National University of Defense Technology, Changsha, 410073, P. R. China

    Yan Zheng & Jian Hua Huang

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  1. Yan Zheng
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  2. Jian Hua Huang
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Correspondence to Yan Zheng.

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Supported by National Natural Science Foundation of China (Grant Nos. 10926096, 10971225)

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Zheng, Y., Huang, J.H. Stochastic stability of FitzHugh-Nagumo systems in infinite lattice perturbed by Gaussian white noise. Acta. Math. Sin.-English Ser. 27, 2143–2152 (2011). https://doi.org/10.1007/s10114-011-9549-1

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  • DOI: https://doi.org/10.1007/s10114-011-9549-1

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