Dynamics and Synchronization of Weakly Coupled Memristive Reaction-Diffusion Neural Networks

TL;DR

This paper introduces a mathematical model for memristive neural networks with reaction-diffusion dynamics, proving conditions for synchronization and demonstrating results through numerical simulations.

Contribution

It develops a new reaction-diffusion model for memristive neural networks and establishes rigorous conditions for exponential synchronization.

Findings

Existence of an absorbing set indicating dissipative dynamics

Conditions for exponential synchronization based on coupling strength

Numerical simulations confirming theoretical results

Abstract

A new mathematical model of memristive neural networks described by the partly diffusive reaction-diffusion equations with weak synaptic coupling is proposed and investigated. Under rather general conditions it is proved that there exists an absorbing set showing the dissipative dynamics of the solution semiflow in the energy space and multiple ultimate bounds. Through uniform estimates and maneuver of integral inequalities and sharp interpolation inequalities on the interneuron differencing equations, it is rigorously proved that exponential synchronization of the neural network solutions at a uniform convergence rate occurs if the coupling strength satisfies a threshold condition expressed by the system parameters. Applications with numerical simulation to the memristive diffusive Hindmarsh-Rose neural networks and FitzHugh-Nagumo neural networks are also shown.