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, th...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.展开更多
基金Supported by National Natural Science Foundation of China （Grant Nos. 10926096, 10971225）
文摘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.
