Adaptive exponential synchronization of impulsive coupled neutral stochastic neural networks with Lévy noise and probabilistic delays under non-Lipschitz conditions

Shuo Ma; Jiangman Li; Qiang Li; Ruonan Liu; Shuo Ma; Jiangman Li; Qiang Li; Ruonan Liu

doi:10.3934/math.20241214

AIMS Mathematics

2024, Volume 9, Issue 9: 24912-24933. doi: 10.3934/math.20241214

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Research article

Adaptive exponential synchronization of impulsive coupled neutral stochastic neural networks with Lévy noise and probabilistic delays under non-Lipschitz conditions

1.
School of Mathematics and Information Science, North Minzu University, Yinchuan, NingXia, 750021, China
2.
School of Information and Artificial Intelligence, Anhui Agricultural University, Hefei, AnHui, 230036, China
3.
Research Center for Applied Mathematics, Anhui Agricultural University, Hefei, AnHui, 230036, China
4.
Department of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou, JiangSu, 221018, China

Received: 14 July 2024 Revised: 02 August 2024 Accepted: 07 August 2024 Published: 26 August 2024
MSC : 93C40, 93D23

In this paper, we investigated the adaptive exponential synchronization problem of impulsive coupled neutral stochastic neural networks with Lévy noise and probabilistic delays under non-Lipschitz conditions. A stochastic variable with a Bernoulli distribution was utilized to transform the information regarding probabilistic delays into a model featuring deterministic time delays and stochastic parameters. In the context of adaptive controllers, exponential synchronization conditions depending on the delay, noise intensity, and impulse factor were derived using Lyapunov-Krasovskii functions, the nature of Lévy noise, and some inequality methods. To provide further support for the proposed approach, two numerical illustrations were presented.
- coupled neutral stochastic neural networks,
- Lévy noise,
- probabilistic delays,
- impulse,
- exponential synchronization
Citation: Shuo Ma, Jiangman Li, Qiang Li, Ruonan Liu. Adaptive exponential synchronization of impulsive coupled neutral stochastic neural networks with Lévy noise and probabilistic delays under non-Lipschitz conditions[J]. AIMS Mathematics, 2024, 9(9): 24912-24933. doi: 10.3934/math.20241214

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Abstract

In this paper, we investigated the adaptive exponential synchronization problem of impulsive coupled neutral stochastic neural networks with Lévy noise and probabilistic delays under non-Lipschitz conditions. A stochastic variable with a Bernoulli distribution was utilized to transform the information regarding probabilistic delays into a model featuring deterministic time delays and stochastic parameters. In the context of adaptive controllers, exponential synchronization conditions depending on the delay, noise intensity, and impulse factor were derived using Lyapunov-Krasovskii functions, the nature of Lévy noise, and some inequality methods. To provide further support for the proposed approach, two numerical illustrations were presented.

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