Exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays

Li Wan; Qinghua Zhou; Hongbo Fu; Qunjiao Zhang; Li Wan; Qinghua Zhou; Hongbo Fu; Qunjiao Zhang

doi:10.3934/math.2021466

AIMS Mathematics

2021, Volume 6, Issue 8: 8030-8043. doi: 10.3934/math.2021466

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Research article

Exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays

1.
Research Centre of Nonlinear Science, Center of Applied Mathematics & Interdisciplinary Sciences, Engineering Technology Research Center of Hubei Province for Clothing Information, School of Mathematics and Physics, Wuhan Textile University, Wuhan, 430073, China
2.
School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, 266061, China

Received: 01 February 2021 Accepted: 22 April 2021 Published: 21 May 2021
MSC : 34D20

This paper investigates the problem for exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays. Different from the existing results, the states of the neurons involve multiple time-varying delays and time derivative of states of neurons also include multiple time-varying delays. The exponential stability of such neutral-type system has not been received enough attention since it is not easy to construct a suitable Lyapunov-Krasovskii functional to analyze the exponential stability of this type of neural system. Novel sufficient conditions of the exponential stability are established by using Lyapunov method and inequality techniques. Compared with some references, the mathematical expression of the neutral-type system is more general and the established algebraic conditions are less conservative. Three examples are given to demonstrate the effectiveness of the theoretical results and compare the established stability conditions to the previous results.
- Hopfield neural network,
- neutral type,
- time-varying delays,
- exponential stability,
- Lyapunov-Krasovskii functional
Citation: Li Wan, Qinghua Zhou, Hongbo Fu, Qunjiao Zhang. Exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays[J]. AIMS Mathematics, 2021, 6(8): 8030-8043. doi: 10.3934/math.2021466

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Abstract

This paper investigates the problem for exponential stability of Hopfield neural networks of neutral type with multiple time-varying delays. Different from the existing results, the states of the neurons involve multiple time-varying delays and time derivative of states of neurons also include multiple time-varying delays. The exponential stability of such neutral-type system has not been received enough attention since it is not easy to construct a suitable Lyapunov-Krasovskii functional to analyze the exponential stability of this type of neural system. Novel sufficient conditions of the exponential stability are established by using Lyapunov method and inequality techniques. Compared with some references, the mathematical expression of the neutral-type system is more general and the established algebraic conditions are less conservative. Three examples are given to demonstrate the effectiveness of the theoretical results and compare the established stability conditions to the previous results.

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