Random Attractors for Non-autonomous Stochastic Lattice FitzHugh-Nagumo Systems with Random Coupled Coefficients

Abstract

In this paper, we study the non-autonomous stochastic lattice FitzHugh-Nagumo system with random coupled coefficients and multiplicative white noise. We consider the existence of random attractors in a weighted space $l_\rho^2 \times l_\rho^2$ for this system, and establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.