Nonuniform behavior and stability of Hopfield neural networks with delay

TL;DR

This paper studies the stability of nonautonomous Hopfield neural networks with delay, providing new theoretical insights and conditions for their behavior and stability.

Contribution

It introduces a novel abstract framework for analyzing nonautonomous delayed equations and applies it to improve stability results for Hopfield neural networks.

Findings

Established bounds for solutions of delayed Hopfield networks.

Improved stability criteria for nonautonomous Hopfield models.

Developed a new abstract approach for delayed differential equations.

Abstract

We obtain a result on the behavior of the solutions of a general nonautonomous Hopfield neural network model with delay, assuming some general bound for the product of consecutive terms in the sequence of neuron charging times and some conditions to control the nonlinear part of the equations. We then apply this result to improve some existent results on the stability of Hopfield models. Our results are based on a new abstract result on the behavior of nonautonomous delayed equations.