Pullback attractor of Hopfield neural networks with multiple time-varying delays

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

doi:10.3934/math.2021435

AIMS Mathematics

2021, Volume 6, Issue 7: 7441-7455. doi: 10.3934/math.2021435

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Research article

Pullback attractor of Hopfield neural networks with multiple time-varying delays

1.
School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, 266061, China
2.
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

Received: 04 March 2021 Accepted: 18 April 2021 Published: 06 May 2021
MSC : 34D20

This paper deals with the attractor problem of Hopfield neural networks with multiple time-varying delays. The mathematical expression of the networks cannot be expressed in the vector-matrix form due to the existence of the multiple delays, which leads to the existence condition of the attractor cannot be easily established by linear matrix inequality approach. We try to derive the existence conditions of the linear matrix inequality form of pullback attractor by employing Lyapunov-Krasovskii functional and inequality techniques. Two examples are given to demonstrate the effectiveness of our theoretical results and illustrate the conditions of the linear matrix inequality form are better than those of the algebraic form.
- Hopfield neural network,
- multiple time-varying delays,
- pullback attractor,
- linear matrix inequality
Citation: Qinghua Zhou, Li Wan, Hongbo Fu, Qunjiao Zhang. Pullback attractor of Hopfield neural networks with multiple time-varying delays[J]. AIMS Mathematics, 2021, 6(7): 7441-7455. doi: 10.3934/math.2021435

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Abstract

This paper deals with the attractor problem of Hopfield neural networks with multiple time-varying delays. The mathematical expression of the networks cannot be expressed in the vector-matrix form due to the existence of the multiple delays, which leads to the existence condition of the attractor cannot be easily established by linear matrix inequality approach. We try to derive the existence conditions of the linear matrix inequality form of pullback attractor by employing Lyapunov-Krasovskii functional and inequality techniques. Two examples are given to demonstrate the effectiveness of our theoretical results and illustrate the conditions of the linear matrix inequality form are better than those of the algebraic form.

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