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Symmetries and cluster synchronization in multilayer networks

Author

Listed:
  • Fabio Rossa

    (University of New Mexico
    Politecnico di Milano)

  • Louis Pecora

    (U.S. Naval Research Laboratory)

  • Karen Blaha

    (University of New Mexico)

  • Afroza Shirin

    (University of New Mexico)

  • Isaac Klickstein

    (University of New Mexico)

  • Francesco Sorrentino

    (University of New Mexico)

Abstract

Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the emergence of cluster synchronization in these networks. We distinguish between independent layer symmetries, which occur in one layer and are independent of the other layers, and dependent layer symmetries, which involve nodes in different layers. We study stability of the cluster synchronous solution by decoupling the problem into a number of independent blocks and assessing stability of each block through a Master Stability Function. We see that blocks associated with dependent layer symmetries have a different structure to the other blocks, which affects the stability of clusters associated with these symmetries. Finally, we validate the theory in a fully analog experiment in which seven electronic oscillators of three kinds are connected with two kinds of coupling.

Suggested Citation

  • Fabio Rossa & Louis Pecora & Karen Blaha & Afroza Shirin & Isaac Klickstein & Francesco Sorrentino, 2020. "Symmetries and cluster synchronization in multilayer networks," Nature Communications, Nature, vol. 11(1), pages 1-17, December.
    • Handle: RePEc:nat:natcom:v:11:y:2020:i:1:d:10.1038_s41467-020-16343-0
    DOI: 10.1038/s41467-020-16343-0
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    Cited by:

    1. Nguyen, Tung T. & Budzinski, Roberto C. & Pasini, Federico W. & Delabays, Robin & Mináč, Ján & Muller, Lyle E., 2023. "Broadcasting solutions on networked systems of phase oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Charley Presigny & Marie-Constance Corsi & Fabrizio De Vico Fallani, 2024. "Node-layer duality in networked systems," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    3. Bosiljka Tadić & Roderick Melnik, 2024. "Fundamental interactions in self-organised critical dynamics on higher order networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-13, June.
    4. 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).
    5. Su, Wenqing & Guo, Xiao & Chang, Xiangyu & Yang, Ying, 2024. "Spectral co-clustering in multi-layer directed networks," Computational Statistics & Data Analysis, Elsevier, vol. 198(C).
    6. Md Sayeed Anwar & Dibakar Ghosh & Nikita Frolov, 2021. "Relay Synchronization in a Weighted Triplex Network," Mathematics, MDPI, vol. 9(17), pages 1-10, September.
    7. Atiyeh Bayani & Fahimeh Nazarimehr & Sajad Jafari & Kirill Kovalenko & Gonzalo Contreras-Aso & Karin Alfaro-Bittner & Rubén J. Sánchez-García & Stefano Boccaletti, 2024. "The transition to synchronization of networked systems," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    8. Anwar, Md Sayeed & Kundu, Srilena & Ghosh, Dibakar, 2021. "Enhancing synchrony in asymmetrically weighted multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    9. Li, Xianghua & Zhen, Xiyuan & Qi, Xin & Han, Huichun & Zhang, Long & Han, Zhen, 2023. "Dynamic community detection based on graph convolutional networks and contrastive learning," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    10. Khanra, Pitambar & Ghosh, Subrata & Alfaro-Bittner, Karin & Kundu, Prosenjit & Boccaletti, Stefano & Hens, Chittaranjan & Pal, Pinaki, 2022. "Identifying symmetries and predicting cluster synchronization in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    11. Pal, Palash Kumar & Bhowmick, Sourav K. & Karmakar, Partha & Ghosh, Dibakar, 2023. "Mixed synchronization in multiplex networks of counter-rotating oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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