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Cluster synchronization of stochastic two-layer delayed neural networks via pinning impulsive control

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Abstract

This paper considers the cluster synchronization of stochastic two-layer delayed neural networks via pinning impulsive control. First, the cluster synchronization of the first layer (leader-layer) network is explored by taking the average state of each subnet as the synchronization target. Then, a pinning impulsive controller is designed to synchronize the second layer (follower-layer) network to the leader-layer network in the mean square cluster sense. Based on the stochastic impulsive analysis and Lyapunov stability theory, some sufficient conditions for cluster synchronization are strictly obtained. At last, the correctness of the theoretical result is illustrated by a numerical example. Compared with previous works, the proposed network model is closer to the real networks and the control strategy is more energy efficient.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 62003189 and 61973189); the China Postdoctoral Science Foundation (Grant No. 2020M672024); the Natural Science Foundation of Shandong Province (Grant Nos. ZR2021MA043 and ZR2022QF075).

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    Junchao Wei, Chuan Zhang, Yingxin Guo & Fei Wang

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  1. Junchao Wei
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  2. Chuan Zhang
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  3. Yingxin Guo
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  4. Fei Wang
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Correspondence to Chuan Zhang.

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Wei, J., Zhang, C., Guo, Y. et al. Cluster synchronization of stochastic two-layer delayed neural networks via pinning impulsive control. J. Appl. Math. Comput. 70, 1193–1210 (2024). https://doi.org/10.1007/s12190-024-02001-x

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