Explosive synchronization in adaptive and multilayer networks

TL;DR

This paper demonstrates that explosive synchronization can occur in adaptive and multilayer networks without specific microscopic correlations, broadening the understanding of the phenomenon beyond previous assumptions.

Contribution

It reveals that explosive synchronization is more general than previously thought, occurring without correlation in adaptive and multilayer networks, supported by analytical and numerical evidence.

Findings

ES occurs without correlation in adaptive networks with local control.

ES appears in multilayer networks regardless of frequency distribution.

Analytical framework explains the mechanisms behind ES in these systems.

Abstract

Explosive synchronization (ES) is nowadays a hot topic of interest in nonlinear science and complex networks. So far, it is conjectured that ES is rooted in the setting of specific microscopic correlation features between the natural frequencies of the networked oscillators and their effective coupling strengths. We show that ES, in fact, is far more general, and can occur in adaptive and multilayer networks also in the absence of such correlation properties. Precisely, we first report evidence of ES in the absence of correlation for networks where a fraction f of the nodes have links adaptively controlled by a local order parameter, and then we extend the study to a variety of two-layer networks with a fraction f of their nodes coupled each other by means of dependency links. In this latter case, we even show that ES sets in, regardless of the differences in the frequency distribution and/or in the topology of connections between the two layers. Finally, we provide a rigorous, analytical, treatment to properly ground all the observed scenario, and to facilitate the understanding of the actual mechanisms at the basis of ES in real-world systems.