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arXiv · 1212.0404

Explosive transitions to synchronization in networked phase oscillators

I. Leyva·I. Sendiña-Nadal·J. Almendral·A. Navas·M. Zanin·D. Papo·J. M. Buldú·S. Boccaletti
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Abstract

We introduce a condition for an ensemble of networked phase oscillators to feature an abrupt, first-order phase transition from an unsynchronized to a synchronized state. This condition is met in a very wide spectrum of situations, and for various oscillators' initial frequency distributions. We show that the occurrence of such transitions is always accompanied by the spontaneous emergence of frequency-degree correlations in random network architectures. We also discuss ways to relax the condition, and to further extend the possibility for the first-order transition to occur, and illustrate how to engineer magnetic-like states of synchronization. Our findings thus indicate how to search for abrupt transitions in real-world applications.

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I. Leyva, I. Sendiña-Nadal, J. Almendral, A. Navas, M. Zanin, D. Papo, J. M. Buldú, S. Boccaletti. 2012-12-03. Explosive transitions to synchronization in networked phase oscillators. https://doi.org/10.1038/srep01281

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