Fixed-time synchronization of mixed-delay fuzzy cellular neural networks with $ L\acute{e}vy $ noise

Tianyi Li; Xiaofeng Xu; Ming Liu; Tianyi Li; Xiaofeng Xu; Ming Liu

doi:10.3934/era.2025090

Electronic Research Archive

2025, Volume 33, Issue 4: 2032-2060. doi: 10.3934/era.2025090

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Research article

Fixed-time synchronization of mixed-delay fuzzy cellular neural networks with $ L\acute{e}vy $ noise

1.
Department of Mathematics, Northeast Forestry University, Harbin 150040, China
2.
Engineering Research Center of Agricultural Microbiology Technology, Ministry of Education, Harbin 150080, China
3.
Heilongjiang Provincial Key Laboratory of Ecological Restoration and Resource Utilization for Cold Region, Harbin 150080, China
4.
School of Mathematical Science, Heilongjiang University, Harbin 150080, China

Received: 22 December 2024 Revised: 08 March 2025 Accepted: 21 March 2025 Published: 11 April 2025

In this paper, we investigate the fixed-time synchronization of fuzzy stochastic cellular neural networks (FSCNNs) with mixed delay and $ L\acute{e}vy $ noise. We designed the feedback controller and adaptive controller for cellular neural networks with $ L\acute{e}vy $ noise to achieve fixed-time synchronization. Using the Lyapunov theory and the $ It\hat{o} $ formula, we established the criterion for fixed-time synchronization of FSCNNs with $ L\acute{e}vy $ noise. Additionally, we obtained the resulting settling time, which is independent of the initial values of the system. The practicality and validity of the theoretical conclusions are demonstrated through two examples. The research results show that when the intensity of random interference is not large, FSCNNs can achieve synchronization through appropriate control means.
- fixed-time synchronization,
- fuzzy cellular neural networks,
- $ L\acute{e}vy $ noise,
- feedback control,
- adaptive control
Citation: Tianyi Li, Xiaofeng Xu, Ming Liu. Fixed-time synchronization of mixed-delay fuzzy cellular neural networks with $ L\acute{e}vy $ noise[J]. Electronic Research Archive, 2025, 33(4): 2032-2060. doi: 10.3934/era.2025090

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Abstract

In this paper, we investigate the fixed-time synchronization of fuzzy stochastic cellular neural networks (FSCNNs) with mixed delay and $ L\acute{e}vy $ noise. We designed the feedback controller and adaptive controller for cellular neural networks with $ L\acute{e}vy $ noise to achieve fixed-time synchronization. Using the Lyapunov theory and the $ It\hat{o} $ formula, we established the criterion for fixed-time synchronization of FSCNNs with $ L\acute{e}vy $ noise. Additionally, we obtained the resulting settling time, which is independent of the initial values of the system. The practicality and validity of the theoretical conclusions are demonstrated through two examples. The research results show that when the intensity of random interference is not large, FSCNNs can achieve synchronization through appropriate control means.

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