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

Yanjie Hong; Wanbiao Ma; Yanjie Hong; Wanbiao Ma

doi:10.3934/mbe.2019249

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4936-4946. doi: 10.3934/mbe.2019249

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

Yanjie Hong ¹,
Wanbiao Ma ^{1,2
,
,}

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

Received: 19 January 2019 Accepted: 05 May 2019 Published: 30 May 2019

In this paper, a class of discrete Hopfield-type neural networks with time delays is considered. 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.
- Hopfield neural networks,
- time delays,
- global attractivity,
- stability,
- difference equation
Citation: Yanjie Hong, Wanbiao Ma. Sufficient and necessary conditions for global attractivity and stability of a class of discrete Hopfield-type neural networks with time delays[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4936-4946. doi: 10.3934/mbe.2019249

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Abstract

In this paper, a class of discrete Hopfield-type neural networks with time delays is considered. 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.

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