Relay synchronization in multiplex networks

TL;DR

This paper investigates relay synchronization in multiplex networks, revealing how distant layers can synchronize via a relay layer, with implications for network control and robustness, supported by analytical, numerical, and experimental results.

Contribution

It provides a systematic analysis of relay synchronization in multiplex networks, including higher order configurations and experimental validation, highlighting the role of network topology and node degree.

Findings

Relay synchronization threshold is reduced in multiplex networks.

Lower degree nodes support relay synchronization more than hubs.

Experimental validation confirms analytical and numerical results.

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.the analytical and numerical findings by means of a multiplex of three layers of electronic circuits.