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Outer Synchronization of Two Muti-Layer Dynamical Complex Networks with Intermittent Pinning Control

Author

Listed:
  • Yi Liang

    (School of Network Security and Information Technology, Yili Normal University, Yining 835000, China
    Key Laboratory of Intelligent Computing Research and Application, Yili Normal University, Yining 835000, China)

  • Yunyun Deng

    (School of Network Security and Information Technology, Yili Normal University, Yining 835000, China
    Key Laboratory of Intelligent Computing Research and Application, Yili Normal University, Yining 835000, China)

  • Chuan Zhang

    (School of Mathematical Science, Qufu Normal University, Qufu 273165, China)

Abstract

This paper regards the outer synchronization of multi-layer dynamical networks with additive couplings via aperiodically intermittent pinning control, in which different layers of each multi-layer network have different topological structures. First, a state-feedback intermittent pinning controller is designed in the drive and response configuration, and sufficient conditions to achieve the outer synchronization are derived based on the Lyapunov stability theory and matrix inequalities. Second, outer synchronization problem of multi-layer networks is discussed by setting an adaptive intermittent pinning controller; an appropriate Lyapunov function is selected to prove the criteria of synchronization between the drive multi-layer network and the response multi-layer network. Finally, three simulation examples are given to show the effectiveness of our control schemes.

Suggested Citation

  • Yi Liang & Yunyun Deng & Chuan Zhang, 2023. "Outer Synchronization of Two Muti-Layer Dynamical Complex Networks with Intermittent Pinning Control," Mathematics, MDPI, vol. 11(16), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3543-:d:1218565
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    References listed on IDEAS

    as
    1. Wang, Guanjun & Cao, Jinde & Lu, Jianquan, 2010. "Outer synchronization between two nonidentical networks with circumstance noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1480-1488.
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    3. Yang, Huilan & Wang, Xin & Zhong, Shouming & Shu, Lan, 2018. "Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 75-85.
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    5. Xudong Hai & Guojian Ren & Yongguang Yu & Conghui Xu, 2019. "Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms," Mathematics, MDPI, vol. 7(5), pages 1-17, May.
    6. M. Hymavathi & Tarek F. Ibrahim & M. Syed Ali & Gani Stamov & Ivanka Stamova & B. A. Younis & Khalid I. Osman, 2022. "Synchronization of Fractional-Order Neural Networks with Time Delays and Reaction-Diffusion Terms via Pinning Control," Mathematics, MDPI, vol. 10(20), pages 1-18, October.
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