Analysis of Remote Synchronization in Complex Networks

TL;DR

This paper demonstrates the widespread occurrence and robustness of remote synchronization in complex networks of coupled oscillators, where non-adjacent nodes synchronize through amplitude modulation of intermediary nodes.

Contribution

It generalizes the concept of remote synchronization from simple motifs to arbitrary complex networks, revealing its underlying mechanisms and prevalence.

Findings

Remote synchronization occurs in various network topologies.

Amplitude modulation of intermediary nodes facilitates remote synchronization.

The phenomenon is robust and more common than previously observed.

Abstract

A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs. We show the existence of a more general dynamical state of remote synchronization in arbitrary networks of coupled oscillators. This state is characterized by the synchronization of pairs of nodes that are not directly connected via a physical link or any sequence of synchronized nodes. This phenomenon is almost negligible in networks of phase oscillators as its underlying mechanism is the modulation of the amplitude of those intermediary nodes between the remotely synchronized units. Our findings thus show the ubiquity and robustness of these states and bridge the gap from their recent observation in simple toy graphs to complex networks.