Sufficient and necessary conditions for global attractivity and stability of a class of discrete Hopfield-type neural networks with time delays

Yan Jie Hong; Wan Biao Ma

doi:10.3934/mbe.2019249

Sufficient and necessary conditions for global attractivity and stability of a class of discrete Hopfield-type neural networks with time delays

Math Biosci Eng. 2019 May 31;16(5):4936-4946. doi: 10.3934/mbe.2019249.

Authors

Yan Jie Hong¹, Wan Biao Ma^{1

2}

Affiliations

¹ Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China.
² Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, University of Science and Technology Beijing, Beijing 100083, P.R. China.

PMID: 31499698
DOI: 10.3934/mbe.2019249

Abstract

In this paper, a class of discrete Hopfield-type neural networks with time delays is consid-ered. Sufficient and necessary conditions for global attractivity and stability of the equilibrium of the discrete Hopfield-type neural networks are given by using a class of n-dimensional nonlinear algebraic equations and M-matrix theory.

Keywords: Hopfield neural networks; difference equation; global attractivity; stability; time delays.

Publication types

Research Support, Non-U.S. Gov't