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

2025/02/16 by José J. Oliveira, Oliveira, José J., Teixeira, Ana Sofia
Computer Science · Physics and Astronomy · #39A12 #39A30 #39A60 #92B20 #Dynamical Systems (math.DS) #FOS: Mathematics #Neural Networks Stability and Synchronization #Neural Networks and Applications #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.2502.11016

openalex publication_date 2025/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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