Random Attractors for the Stochastic FitzHugh-Nagumo System on Unbounded Domains

TL;DR

This paper proves the existence of a random attractor for the stochastic FitzHugh-Nagumo system on unbounded domains, using uniform estimates and a cut-off technique to establish pullback asymptotic compactness.

Contribution

It introduces a method to demonstrate the existence of random attractors for stochastic systems on unbounded domains, expanding the understanding of their long-term behavior.

Findings

Existence of a random attractor for the system.

Establishment of pullback asymptotic compactness.

Use of cut-off technique for uniform estimates.

Abstract

The existence of a random attractor for the stochastic FitzHugh-Nagumo system defined on an unbounded domain is established. The pullback asymptotic compactness of the stochastic system is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique.