Source-linked AI summary
Explosive synchronization in adaptive and multilayer networks
Xiyun Zhang, Stefano Boccaletti, Shuguang Guan, Zonghua Liu
TL;DR
The paper asks whether explosive synchronization requires positive microscopic correlations between natural frequencies and effective couplings. It studies adaptive and dependency-coupled multilayer networks analytically and numerically, finding ES without those correlations and identifying suppression of giant-cluster formation as the common mechanism.
Problem
Prior work attributed explosive synchronization to positive correlations between oscillators’ natural frequencies and degrees or effective coupling strengths.
Method
The study combines simulations of adaptively controlled single networks and dependency-linked two-layer networks with a mean-field analytical treatment.
Results
Explosive synchronization occurs without positive frequency–coupling correlations, including across multilayer networks with varied topologies and frequency distributions.
Takeaways & Limitations
The paper concludes that ES requires a microscopic suppressive rule preventing formation of a giant synchronization cluster, rather than a specific correlation pattern.
Takeaways & Limitations
The analytical treatment assumes factorized joint distributions h(k,ω)=P(k)g(ω) for network degree and frequency.
Abstract
from arXiv · showhide
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.