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Pinning impulsive cluster synchronization of uncertain complex dynamical networks with multiple time-varying delays and impulsive effects

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  • Fan, Hongguang
  • Shi, Kaibo
  • Zhao, Yi

Abstract

The pinning impulsive cluster synchronization problem of uncertain complex community networks with impulsive effects, internal delay and coupling delay is studied in this paper. Particularly, the local dynamics of nodes in different communities are assumed to be nonidentical and two kinds of delays are all time-varying. A novel impulsive comparison principle with multiple time-varying delays is established to conquer the difficulties caused by various delays and impulsive effects. Based on the Lyapunov stability theory and pinning impulsive control techniques, some sufficient conditions depending on impulsive intervals and delays are derived to guarantee cluster synchronization of the community networks by pinning a small fractional of network nodes. The upper bound of the internal delay and coupling delay can be estimated by the obtained conditions. The theoretical results in this paper can be seen as extensions of the previous related works. Finally, a numerical simulation is presented to illustrate the validity of our results.

Suggested Citation

  • Fan, Hongguang & Shi, Kaibo & Zhao, Yi, 2022. "Pinning impulsive cluster synchronization of uncertain complex dynamical networks with multiple time-varying delays and impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    • Handle: RePEc:eee:phsmap:v:587:y:2022:i:c:s0378437121008074
    DOI: 10.1016/j.physa.2021.126534
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    Cited by:

    1. Liu, Shuang & Xu, Tianwei & Wang, Qingyun & Yang, Yan, 2024. "The impulsive synchronization of multiplex networks with mixed delays and dual uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 141-163.
    2. Hongguang Fan & Yue Rao & Kaibo Shi & Hui Wen, 2023. "Global Synchronization of Fractional-Order Multi-Delay Coupled Neural Networks with Multi-Link Complicated Structures via Hybrid Impulsive Control," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    3. Hongguang Fan & Jiahui Tang & Kaibo Shi & Yi Zhao & Hui Wen, 2023. "Delayed Impulsive Control for μ -Synchronization of Nonlinear Multi-Weighted Complex Networks with Uncertain Parameter Perturbation and Unbounded Delays," Mathematics, MDPI, vol. 11(1), pages 1-17, January.
    4. Fan, Hongguang & Shi, Kaibo & Zhao, Yi, 2022. "Global μ-synchronization for nonlinear complex networks with unbounded multiple time delays and uncertainties via impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    5. Yong Tang & Lang Zhou & Jiahui Tang & Yue Rao & Hongguang Fan & Jihong Zhu, 2023. "Hybrid Impulsive Pinning Control for Mean Square Synchronization of Uncertain Multi-Link Complex Networks with Stochastic Characteristics and Hybrid Delays," Mathematics, MDPI, vol. 11(7), pages 1-18, April.

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