Global attractivity criteria for a discrete-time Hopfield neural network model with unbounded delays via singular M-matrices

TL;DR

This paper develops new global attractivity criteria for discrete-time Hopfield neural networks with infinite delays, using singular M-matrices, applicable to both bounded and unbounded activation functions.

Contribution

It introduces novel attractivity conditions involving singular M-matrices for non-autonomous neural networks with delays, expanding previous stability analysis methods.

Findings

Criteria applicable to bounded activation functions using non-invertible M-matrices

Criteria for unbounded activation functions involving irreducible singular M-matrices

Numerical simulations demonstrating the effectiveness of the proposed criteria

Abstract

In this work, we establish two global attractivity criteria for a multidimensional discrete-time non-autonomous Hopfield neural network model with infinite delays and delays in the leakage terms. The first criterion, which applies when the activation functions are bounded, is based on M-matrices that are not necessarily invertible. The second criterion, relevant for unbounded activation functions, requires that a related singular M-matrix be irreducible. We contrast our findings with existing results in the literature and present numerical simulations to illustrate the efficacy of the proposed criteria.