Average-delay impulsive control for synchronization of uncertain chaotic neural networks with variable delay impulses

Biwen Li; Yujie Liu; Biwen Li; Yujie Liu

doi:10.3934/mbe.2025052

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 6: 1382-1398. doi: 10.3934/mbe.2025052

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Average-delay impulsive control for synchronization of uncertain chaotic neural networks with variable delay impulses

Biwen Li ,
Yujie Liu ^,

Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Academic Editor: Mingji Zhang

Received: 18 March 2025 Revised: 13 April 2025 Accepted: 23 April 2025 Published: 30 April 2025

This paper investigated the synchronization issue of uncertain chaotic neural networks (CNNs) using a delayed impulsive control approach. To address the disturbances caused by parameter uncertainty and the flexibility of impulsive delays, the concept of average impulsive delay (AID) and average impulsive interval (AII) were utilized to handle the delays as a whole. Under the condition that the norms of uncertain parameters are bounded, the synchronization criteria for uncertain CNNs were derived based on linear matrix inequalities (LMIs). Specifically, we relaxed the constraints on the delay in the impulsive control inputs, thus allowing it to flexibly vary without being bound by some conditions, which provides a broader applicability compared to most existing results. Additionally, the results show that delayed impulses can facilitate the synchronization of uncertain CNNs. Finally, the validity of the theoretical results was verified through a numerical example.
- delayed impulsive control,
- uncertain chaotic neural networks,
- synchronization,
- average impulsive delay (AID),
- average impulsive interval (AII)
Citation: Biwen Li, Yujie Liu. Average-delay impulsive control for synchronization of uncertain chaotic neural networks with variable delay impulses[J]. Mathematical Biosciences and Engineering, 2025, 22(6): 1382-1398. doi: 10.3934/mbe.2025052

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Abstract

This paper investigated the synchronization issue of uncertain chaotic neural networks (CNNs) using a delayed impulsive control approach. To address the disturbances caused by parameter uncertainty and the flexibility of impulsive delays, the concept of average impulsive delay (AID) and average impulsive interval (AII) were utilized to handle the delays as a whole. Under the condition that the norms of uncertain parameters are bounded, the synchronization criteria for uncertain CNNs were derived based on linear matrix inequalities (LMIs). Specifically, we relaxed the constraints on the delay in the impulsive control inputs, thus allowing it to flexibly vary without being bound by some conditions, which provides a broader applicability compared to most existing results. Additionally, the results show that delayed impulses can facilitate the synchronization of uncertain CNNs. Finally, the validity of the theoretical results was verified through a numerical example.

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