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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

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

Special Issues: Mathematical Modeling to Solve the Problems in Life Sciences

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.
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Keywords 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. Mathematical Biosciences and Engineering, 2019, 16(5): 4936-4946. doi: 10.3934/mbe.2019249

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