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Synchronizability of Multi-Layer Variable Coupling Windmill-Type Networks

Author

Listed:
  • Jian Zhu

    (Department of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China)

  • Da Huang

    (Department of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China)

  • Haijun Jiang

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China)

  • Jicheng Bian

    (Department of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China)

  • Zhiyong Yu

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China)

Abstract

The system model on synchronizability problem of complex networks with multi-layer structure is closer to the real network than the usual single-layer case. Based on the master stability equation (MSF), this paper studies the eigenvalue spectrum of two k-layer variable coupling windmill-type networks. In the case of bounded and unbounded synchronization domain, the relationships between the synchronizability of the layered windmill-type networks and network parameters, such as the numbers of nodes and layers, inter-layers coupling strength, are studied. The simulation of the synchronizability of the layered windmill-type networks are given, and they verify the theoretical results well. Finally, the optimization schemes of the synchronizability are given from the perspective of single-layer and multi-layer networks, and it was found that the synchronizability of the layered windmill-type networks can be improved by changing the parameters appropriately.

Suggested Citation

  • Jian Zhu & Da Huang & Haijun Jiang & Jicheng Bian & Zhiyong Yu, 2021. "Synchronizability of Multi-Layer Variable Coupling Windmill-Type Networks," Mathematics, MDPI, vol. 9(21), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2721-:d:665544
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    References listed on IDEAS

    as
    1. Mingming Xu & Jin Zhou & Jun-an Lu & Xiaoqun Wu, 2015. "Synchronizability of two-layer networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(9), pages 1-6, September.
    2. Deng, Yang & Jia, Zhen & Deng, Guangming & Zhang, Qiongfen, 2020. "Eigenvalue spectrum and synchronizability of multiplex chain networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. Yang Deng & Zhen Jia & Feimei Yang, 2020. "Synchronizability of Multilayer Star and Star-Ring Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-20, April.
    4. Yuanyuan Li & Jie Zhong & Jianquan Lu & Zhen Wang & Fuad E. Alssadi, 2018. "On Robust Synchronization of Drive-Response Boolean Control Networks with Disturbances," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-9, August.
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