This paper is concerned with the Wong–Zakai approximations given by a stationary process via the Wiener shift and their associated long term behavior of stochastic FitzHugh–Nagumo system driven by white noise. We prove the existence and uniqueness of pullback random attractors for the approximate system under much weaker conditions than the original system. When the system is driven by additive white noise, we also prove the convergence of solutions of Wong–Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as the size of approximation approaches zero.

中文翻译：

---

随机 FitzHugh-Nagumo 系统的 Wong-Zakai 近似和长期行为

本文关注由平稳过程通过维纳位移给出的 Wong-Zakai 近似值及其相关的白噪声驱动的随机 FitzHugh-Nagumo 系统的长期行为。我们证明了在比原始系统弱得多的条件下，近似系统的回拉随机吸引子的存在性和唯一性。当系统由加性白噪声驱动时，我们还证明了 Wong-Zakai 近似解的收敛性和近似随机系统的随机吸引子的上半连续性，当近似大小接近零时。