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

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.