Document Code:

111512

First Author:

Shuang Yang

Journal:

Journal of Mathematical Physics

Included Journals:

SCI

Place of Publication:

UNITED STATES

Volume:

63

Issue:

11

ISSN No.:

0022-2488

Key Words:

Random delayed lattice system; FitzHugh-Nagumo system; Nonlinear Wong-Zakai noise; Pullback random attractor; Upper semicontinuity

DOI number:

10.1063/5.0125383

Date of Publication:

2022-11-01

Abstract:

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

Links to published journals:

https://doi.org/10.1063/5.0125383