Global Dynamics of Diffusive Hindmarsh-Rose Equations with Memristors

TL;DR

This paper investigates the global behavior of a new neuron model incorporating memristors, proving the existence of a global attractor and providing explicit bounds based on model parameters.

Contribution

It establishes the existence and regularity of a global attractor for the diffusive Hindmarsh-Rose equations with memristors, a novel neuron model.

Findings

Existence of a global attractor is proven.

Explicit bounds for the attractor are derived.

Higher-order dissipative properties are demonstrated.

Abstract

Global dynamics of the diffusive Hindmarsh-Rose equations with memristor as a new proposed model for neuron dynamics are investigated in this paper. We prove the existence and regularity of a global attractor for the solution semiflow through uniform analytic estimates showing the higher-order dissipative property and the asymptotically compact characteristics of the solution semiflow by the approach of Kolmogorov-Riesz theorem. The quantitative bounds of the regions containing this global attractor respectively in the state space and in the regular space are explicitly expressed by the model parameters.