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

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.

arXiv commentarXiv admin note: text overlap with arXiv:2409.17548, arXiv:2412.19428 by other authors