Explosive synchronization in adaptive and multilayer networks

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.

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• Explosive Synchronization Transitions in Scale-free Networks
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Explosive first-order transition to synchrony in networked chaotic oscillators
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Cited by in corpus (2)

• Effect of assortative mixing in the second-order Kuramoto model
• Two Types of Discontinuous Percolation Transitions in Cluster Merging Processes