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.
Highlights
Synchronization is one of the most important collective phenomena in nature
We perform a systematic study of inter-layer relay synchronization in a multiplex network, where distant layers synchronize their dynamics while their intra-layer motion remains unsynchronized
Layers are coupled in a multiplex configuration, and the dynamical evolution of the system is described by the following equations:
Summary
Synchronization is one of the most important collective phenomena in nature. It can be observed in natural, social and technological systems, and it became one of the most active research topics in network science[1,2,3]. The robustness of the relay synchronization against de-multiplexing the layers is reported, revealing the key role of low degree nodes in maintaining the layers coordination.
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