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Outer Synchronization of Complex-Variable Networks with Complex Coupling via Impulsive Pinning Control

Author

Listed:
  • Yanjie Ji

    (School of Mathematics and Statistic, Jiangxi Normal University, Nanchang 330022, China)

  • Zhaoyan Wu

    (School of Mathematics and Statistic, Jiangxi Normal University, Nanchang 330022, China)

Abstract

In this paper, outer synchronization of complex-variable networks with complex coupling is considered. Sufficient conditions for achieving outer synchronization using static impulsive pinning controllers are first derived according to the Lyapunov function method and stability theory of impulsive differential equations. From these conditions, the necessary impulsive gains and intervals for given networks can be easily calculated. Further, an adaptive strategy is introduced to design universal controllers and avoid repeated calculations for different networks. Notably, the estimation algorithms of the impulsive gains and intervals are provided. Finally, three numerical examples are performed to verify the effectiveness of the main results.

Suggested Citation

  • Yanjie Ji & Zhaoyan Wu, 2021. "Outer Synchronization of Complex-Variable Networks with Complex Coupling via Impulsive Pinning Control," Mathematics, MDPI, vol. 9(17), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2110-:d:626914
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    References listed on IDEAS

    as
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    2. Li, Chengren & Lü, Ling & Yang, Yiming & Zhou, Shuang & Hong, Yixuan, 2018. "Research on outer synchronization between uncertain time-varying networks with different node number," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2301-2309.
    3. Leng, Hui & Wu, Zhaoyan, 2019. "Impulsive synchronization of complex-variable network with distributed time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    4. Xuefei Wu & Jianwen Feng & Zhe Nie & Guang Li, 2021. "Outer Synchronization of Drive-Response Complex-Valued Complex Networks via Intermittent Pinning Control," Complexity, Hindawi, vol. 2021, pages 1-10, February.
    5. Zhaoyan Wu & Xinchu Fu, 2013. "Synchronization Of Complex-Variable Dynamical Networks With Complex Coupling," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-13.
    6. Li, Xuechen & Wang, Nan & Lu, Jianquan & Alsaadi, Fuad E., 2019. "Pinning outer synchronization of partially coupled dynamical networks with complex inner coupling matrices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 497-509.
    7. Pan, Jinsong & Zhang, Zhengqiu, 2021. "Finite-time synchronization for delayed complex-valued neural networks via the exponential-type controllers of time variable," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    Full references (including those not matched with items on IDEAS)

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