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

• Author(s): Oliveira, José J. ; Teixeira, Ana Sofia
• Date: 2025
• Persistent ID: https://hdl.handle.net/1822/97465
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Hopfield neural network model; Global attractivity; Difference equation; Infinite time delay; M-matrix; Irreducible matrix
• Document Type: Journal article
• Language: English
• Contributor(s): Universidade do Minho

Description

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 -matrices that are not necessarily invertible. The second criterion, relevant for unbounded activation functions, requires that a related singular -matrix be irreducible. We contrast our findings with existing results in the literature and present numerical simulations to illustrate the novelty of the proposed criteria.