Relay Synchronization in a Weighted Triplex Network

Md Sayeed Anwar, Dibakar Ghosh and Nikita Frolov
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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

Mathematics, 2021, vol. 9, issue 17, 1-10

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.

Keywords: relay synchronization; multi-layer networks; hubs-attracting; hubs-repelling; master stability function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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