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Phys Rev Lett. 2015 Jan 23;114(3):038701. Epub 2015 Jan 21.

Explosive synchronization in adaptive and multilayer networks.

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Department of Physics, East China Normal University, Shanghai 200062, China.
CNR-Institute of Complex Systems, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Florence, Italy and The Italian Embassy in Israel, 25 Hamered Street, 68125 Tel Aviv, Israel.


At this time, explosive synchronization (ES) of networked oscillators is thought of as being rooted in the setting of specific microscopic correlation features between the natural frequencies of the oscillators and their effective coupling strengths. We show that ES is, in fact, far more general and can occur in adaptive and multilayer networks in the absence of such correlation properties. We first report evidence of ES for single-layer networks where a fraction f of the nodes have links adaptively controlled by a local order parameter, and we then extend the study to a variety of two-layer networks with a fraction f of their nodes coupled with each other by means of dependency links. In the latter case, we give evidence of ES regardless of the differences in the frequency distribution, in the topology of connections between the layers, or both. Finally, we provide a rigorous, analytical treatment to properly ground all of the observed scenarios and to advance the understanding of the actual mechanisms at the basis of ES in real-world systems.

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