Global Attractors for Hindmarsh-Rose Equations in Neurodynamics

TL;DR

This paper investigates the long-term behavior of Hindmarsh-Rose equations used in neurodynamics, establishing the existence of global attractors and their regularity through mathematical estimates.

Contribution

It proves the existence and regularity of global attractors for both diffusive and partly diffusive Hindmarsh-Rose equations, advancing understanding of their asymptotic dynamics.

Findings

Existence of global attractors established

Regularity of attractors proved

Asymptotic compactness demonstrated

Abstract

Global dynamics of the diffusive and partly diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain originated in neurodynamics are investigated in this paper. The existence of global attractors as well as the regularity are proved through various uniform estimates showing the dissipative properties and the asymptotically compact characteristics, especially for the partly diffusive Hindmarsh-Rose equations by means of the Kolmogorov-Riesz theorem.