Quantum mechanics

World Wide Web

Materials science

Layer (electronics)

Stability (learning theory)

Relay

Weighting

Power (physics)

Computer science

Acoustics

Complex network

Computer network

Physics

Relay channel

Organic chemistry

Link Access Procedure for Frame Relay

Mathematics

Synchronization networks

Synchronization (alternating current)

Composite material

Combinatorics

Chemistry

Channel (broadcasting)

Topology (electrical circuits)

Machine learning

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.

Relay Synchronization in a Weighted Triplex Network