Wong–Zakai approximations of the non-autonomous stochastic FitzHugh–Nagumo system on RN in higher regular spaces

Abstract

In this paper, we consider the Wong–Zakai approximations of a non-autonomous stochastic FitzHugh–Nagumo system driven by a multiplicative white noise with an arbitrary intensity. The convergence of solutions of the path-wise deterministic system to that of the corresponding stochastic system is established in higher regular spaces by means of a new iteration technique and an optimal multiplier at different stages. Furthermore, we prove that the random attractor of the path-wise deterministic system converges to that of the non-autonomous stochastic FitzHugh–Nagumo system in higher regular spaces when the size of approximation vanishes, with much looser conditions on the nonlinearity.