Pullback measure attractors for non-autonomous stochastic FitzHugh-Nagumo system with distribution dependence on unbounded domains

TL;DR

This paper investigates the long-term behavior of a stochastic FitzHugh-Nagumo neural model with distribution dependence on unbounded domains, establishing well-posedness and the existence of unique pullback measure attractors.

Contribution

It introduces a novel analysis of non-autonomous stochastic systems with distribution dependence, proving existence and uniqueness of attractors on unbounded domains.

Findings

Well-posedness of solutions established

Existence and uniqueness of pullback measure attractors proven

Application of splitting techniques and Vitali's theorem

Abstract

This paper is primarily focused on the asymptotic dynamics of a non-autonomous stochastic FitzHugh-Nagumo system with distribution dependence, specifically on unbounded domains $\mathbb{R}^{n}$. Initially, we establish the well-posedness of solutions for the FitzHugh-Nagumo system with distribution dependence by utilizing the Banach fixed-point theorem. Subsequently, we demonstrate the existence and uniqueness of pullback measure attractors for this system through the application of splitting techniques, tail-end estimates and Vitali's theorem.