Relay Synchronization in a Weighted Triplex Network

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.

Stability of synchronization in simplicial complexes with multiple interaction layers

“…Our investigation is based on the most prevalent and well-studied synchronization behavior, namely, the com-plete synchronization phenomenon. However, many additional types of synchrony occurs in the systems with multiple interaction layers such as chimeras [80], cluster synchronization [81], relay synchronization [69], etc. All of these synchronization states have been investigated in multilayer systems with solely pairwise interactions.…”

Interlayer antisynchronization in degree-biased duplex networks

“…This rescaled unsymmetric hub-attracting matrix reflects the tendency to produce a strong influence on the low-degree neighbors by the high-degree nodes [63]. We can inspect the reverse scenario of biased domination from low to high-degree nodes with the hub-repelling matrix by considering β = −1 [61,63]. However, the matrix remains unaltered for β = 0, i.e., we have à [α] i j = A [α] i j for β = 0.…”

Synchronization Induced by Layer Mismatch in Multiplex Networks

“…Diverse forms of synchronization patterns have been detected in multiplex networks with static or temporal interactions, including-but not limited to-cluster synchronization [28,29], explosive synchronization [30], chimera states [31], intralayer synchronization [32,33], interlayer synchronization [34][35][36], and relay synchronization [37][38][39]. Recently, the study of synchronization in multilayer networks has also been extended to include higher-order interactions [36,40].…”