Exponential synchronization of neural networks with mixed delays under impulsive control

Wanshun Zhao; Kelin Li; Yanchao Shi; Wanshun Zhao; Kelin Li; Yanchao Shi

doi:10.3934/era.2024244

Electronic Research Archive

2024, Volume 32, Issue 9: 5287-5305. doi: 10.3934/era.2024244

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Research article

Exponential synchronization of neural networks with mixed delays under impulsive control

1.
College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
2.
School of Science, Southwest Petroleum University, Chengdu 610500, China

Received: 14 July 2024 Revised: 02 September 2024 Accepted: 05 September 2024 Published: 13 September 2024

In this paper, the exponential synchronization problem of a class of neural networks with mixed delays under impulsive control is studied. Combining the impulsive comparison principle and the concept of an average impulsive interval, two impulsive differential inequalities with mixed delays are discussed, and the sufficient conditions for the existence of exponential decay are obtained. Based on two different impulsive control strategies, and then by means of the Lyapunov function, the inequality technique, and these two new inequalities, a set of sufficient conditions are derived to ensure the synchronization of the drive and response systems. In order to prove the effectiveness of the proposed control scheme, two numerical examples are given to prove its practicability and effectiveness.
- neural networks,
- impulsive differential inequalities,
- exponential synchronization,
- delay,
- impulsive control
Citation: Wanshun Zhao, Kelin Li, Yanchao Shi. Exponential synchronization of neural networks with mixed delays under impulsive control[J]. Electronic Research Archive, 2024, 32(9): 5287-5305. doi: 10.3934/era.2024244

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Abstract

In this paper, the exponential synchronization problem of a class of neural networks with mixed delays under impulsive control is studied. Combining the impulsive comparison principle and the concept of an average impulsive interval, two impulsive differential inequalities with mixed delays are discussed, and the sufficient conditions for the existence of exponential decay are obtained. Based on two different impulsive control strategies, and then by means of the Lyapunov function, the inequality technique, and these two new inequalities, a set of sufficient conditions are derived to ensure the synchronization of the drive and response systems. In order to prove the effectiveness of the proposed control scheme, two numerical examples are given to prove its practicability and effectiveness.

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