Synchronization of Memristive FitzHugh-Nagumo Neural Networks

TL;DR

This paper introduces a mathematical model of neural networks with memristors and linear synaptic coupling, proving conditions for exponential synchronization and demonstrating results through simulations.

Contribution

It presents a new memristive FitzHugh-Nagumo neural network model and establishes explicit conditions for exponential synchronization.

Findings

Existence of absorbing set in the energy space.

Neural networks exhibit exponential synchronization under certain conditions.

Numerical simulations confirm theoretical results.

Abstract

A new mathematical model of neural networks described by diffusive FitzHugh-Nagumo equations with memristors and linear synaptic coupling is proposed and investigated. The existence of absorbing set for the solution semiflow in the energy space is proved and global dynamics of the memristive neural networks are dissipative. Through uniform estimates and maneuver of integral inequalities on the interneuron difference equations, it is shown that exponential synchronization of the neural network at a uniform convergence rate occurs if the coupling strength satisfies a threshold condition explicitly expressed by the system parameters, which is illustrated by an example and numerical simulation experiments.