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Eigenvalue spectrum and synchronizability of multiplex chain networks

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  • Deng, Yang
  • Jia, Zhen
  • Deng, Guangming
  • Zhang, Qiongfen

Abstract

Synchronization phenomena are of broad interest across disciplines and increasingly of interest in a multiplex network setting. In this paper, the problem of synchronization of two multiplex chain networks is investigated, according to the master stability function method. We define two kinds of multiplex chain networks according to different coupling modes: one is a class of the multiplex chain networks with one-to-one undirected coupling between layers(Networks-A), and the other is a class of the multiplex chain networks with one-to-one unidirectional coupling between layers(Networks-B). The eigenvalue spectrum of the supra-Laplacian matrices of two kinds of the networks is strictly derived theoretically, and the relationships between the structural parameters and synchronizability of the networks are further revealed. The structural parameter values of the networks to achieve the optimal synchronizability are obtained. Numerical examples are also provided to verify the effectiveness of theoretical analysis.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315043
    DOI: 10.1016/j.physa.2019.122631
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    References listed on IDEAS

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    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. Wang, Pei & Xu, Shuang, 2017. "Spectral coarse grained controllability of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 168-176.
    3. Jia, Zhen & Zeng, Lang & Wang, Ying-Ying & Wang, Pei, 2019. "Optimization algorithms for spectral coarse-graining of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 925-935.
    4. Long, Yong-Shang & Jia, Zhen & Wang, Ying-Ying, 2018. "Coarse graining method based on generalized degree in complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 655-665.
    5. Siudem, Grzegorz & Hołyst, Janusz A., 2019. "Diffusion on hierarchical systems of weakly-coupled networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 675-686.
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    Cited by:

    1. Yang, Qing-Lin & Wang, Li-Fu & Zhao, Guo-Tao & Guo, Ge, 2020. "A coarse graining algorithm based on m-order degree in complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    2. 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.

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