Relay synchronization in multiplex networks

TLDR

Relay synchronization enables distant coordination between non‑adjacent oscillators in a network. The study systematically investigates relay synchronization in multiplex networks, where a relay layer mediates inter‑layer synchronization between distant layers. The authors use first‑order perturbative analysis and experimental validation with a three‑layer electronic circuit multiplex to identify dynamical and topological dependencies of relay synchronization. Relay synchronization can be extended to higher‑order configurations under symmetry, with a reduced threshold in multiplexes, mainly supported by low‑degree nodes, and this was experimentally confirmed in a three‑layer electronic circuit multiplex.

Abstract

Relay (or remote) synchronization between two not directly connected oscillators in a network is an important feature allowing distant coordination. In this work, we report a systematic study of this phenomenon in multiplex networks, where inter-layer synchronization occurs between distant layers mediated by a relay layer that acts as a transmitter. We show that this transmission can be extended to higher order relay configurations, provided symmetry conditions are preserved. By first order perturbative analysis, we identify the dynamical and topological dependencies of relay synchronization in a multiplex. We find that the relay synchronization threshold is considerably reduced in a multiplex configuration, and that such synchronous state is mostly supported by the lower degree nodes of the outer layers, while hubs can be de-multiplexed without affecting overall coherence. Finally, we experimentally validated the analytical and numerical findings by means of a multiplex of three layers of electronic circuits.