Dynamical stability of random delayed FitzHugh–Nagumo lattice systems driven by nonlinear Wong–Zakai noise

In this paper, two problems related to FitzHugh–Nagumo lattice systems are analyzed. The first one is concerned with the asymptotic behavior of random delayed driven by nonlinear Wong–Zakai noise. We obtain a new result ensuring that such system approximates corresponding deterministic when correlation time noise goes infinity rather than zero. prove existence tempered attractors for drift function and diffusion term. pullback compactness solutions proved thanks Ascoli–Arzelà theorem uniform tail-estimates. then show upper semicontinuity as tends infinity. As second problem, we consider version previous model study convergence delay approaches That is, non-delayed proved.