Synchronization of nonautonomous neural networks with Caputo derivative and time delay

Lili Jia; Changyou Wang; Zongxin Lei; Lili Jia; Changyou Wang; Zongxin Lei

doi:10.3934/nhm.2023013

Networks and Heterogeneous Media

2023, Volume 18, Issue 1: 341-358. doi: 10.3934/nhm.2023013

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Synchronization of nonautonomous neural networks with Caputo derivative and time delay

1.
Dianchi College of Yunnan University, Kunming, Yunnan 650228, P.R. China
2.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, P.R. China

Received: 09 November 2022 Revised: 12 December 2022 Accepted: 18 December 2022 Published: 23 December 2022

The synchronization problem of delayed nonautonomous neural networks with Caputo derivative is studied in this article. Firstly, new neural networks are proposed by introducing variable parameters into known models, and the analytical formula of the synchronous controller is given according to the new neural networks. Secondly, from the drive-response systems corresponding to the above delayed neural networks, their error system is obtained. Thirdly, by constructing the Lyapunov function and utilizing the Razumikhin-type stability theorem, the asymptotic stability of zero solution for the error system is verified, and some sufficient conditions are achieved to ensure the global asymptotic synchronization of studied neural networks. Finally, some numerical simulations are given to show the availability and feasibility of our obtained results.
- synchronization,
- delayed,
- Caputo derivative,
- neural networks,
- nonautonomous
Citation: Lili Jia, Changyou Wang, Zongxin Lei. Synchronization of nonautonomous neural networks with Caputo derivative and time delay[J]. Networks and Heterogeneous Media, 2023, 18(1): 341-358. doi: 10.3934/nhm.2023013

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Abstract

The synchronization problem of delayed nonautonomous neural networks with Caputo derivative is studied in this article. Firstly, new neural networks are proposed by introducing variable parameters into known models, and the analytical formula of the synchronous controller is given according to the new neural networks. Secondly, from the drive-response systems corresponding to the above delayed neural networks, their error system is obtained. Thirdly, by constructing the Lyapunov function and utilizing the Razumikhin-type stability theorem, the asymptotic stability of zero solution for the error system is verified, and some sufficient conditions are achieved to ensure the global asymptotic synchronization of studied neural networks. Finally, some numerical simulations are given to show the availability and feasibility of our obtained results.

References

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