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Relay Synchronization in a Weighted Triplex Network

Author

Listed:
  • Md Sayeed Anwar

    (Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India)

  • Dibakar Ghosh

    (Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India)

  • Nikita Frolov

    (Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, Russia
    Center for Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, 236041 Kaliningrad, Russia)

Abstract

Relay synchronization in multi-layer networks implies inter-layer synchronization between two indirectly connected layers through a relay layer. In this work, we study the relay synchronization in a three-layer multiplex network by introducing degree-based weighting mechanisms. The mechanism of within-layer connectivity may be hubs-repelling or hubs-attracting whenever low-degree or high-degree nodes receive strong influence. We adjust the remote layers to hubs-attracting coupling, whereas the relay layer may be unweighted, hubs-repelling, or hubs-attracting network. We establish that relay synchronization is improved when the relay layer is hubs-repelling compared to the other cases. We determine analytically necessary stability conditions of relay synchronization state using the master stability function approach. Finally, we explore the relation between synchronization and the topological property of the relay layer. We find that a higher clustering coefficient hinders synchronizability, and vice versa. We also look into the intra-layer synchronization in the proposed weighted triplex network and establish that intra-layer synchronization occurs in a wider range when relay layer is hubs-attracting.

Suggested Citation

  • Md Sayeed Anwar & Dibakar Ghosh & Nikita Frolov, 2021. "Relay Synchronization in a Weighted Triplex Network," Mathematics, MDPI, vol. 9(17), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2135-:d:627801
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    References listed on IDEAS

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    2. 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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