Intra-layer synchronization in multiplex networks

TL;DR

This paper investigates a new synchronization regime in multiplex networks where oscillators in the top layer synchronize independently of the medium, with conditions on the medium's topology and a density-dependent threshold.

Contribution

It introduces a novel intra-layer synchronization regime in multiplex networks with inhomogeneous media, expanding understanding of indirect oscillator coupling.

Findings

Intra-layer coherence can occur without inter-layer coherence.

Synchronization depends on the medium's topology supporting oscillator synchronization.

A density-dependent threshold similar to quorum sensing is identified.

Abstract

We study synchronization of $N$ oscillators indirectly coupled through a medium which is inhomogeneous and has its own dynamics. The system is formalized in terms of a multilayer network, where the top layer is made of disconnected oscillators and the bottom one, modeling the medium, consists of oscillators coupled according to a given topology. The different dynamics of the medium and the top layer is accounted by including a frequency mismatch between them. We show a novel regime of synchronization as intra-layer coherence does not necessarily require inter-layer coherence. This regime appears under mild conditions on the bottom layer: arbitrary topologies may be considered, provided that they support synchronization of the oscillators of the medium. The existence of a density-dependent threshold as in quorum-sensing phenomena is also demonstrated.