Explosive transitions to synchronization in networks of phase oscillators

• Published in: Scientific reports Vol. 3; no. 1; p. 1281
• Main Authors: Leyva, I., Navas, A., Sendiña-Nadal, I., Almendral, J. A., Buldú, J. M., Zanin, M., Papo, D., Boccaletti, S.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 15.02.2013; Nature Publishing Group
• Subjects: 631/553/2693; 631/553/2712; 631/553/2717; 639/766/408/530; Humanities and Social Sciences; multidisciplinary; Oscillators; Phase transitions; Science; Synchronization
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/srep01281

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. The occurrence of a first-order phase transition to synchronization of an ensemble of networked phase oscillators was reported, so far, for very particular network architectures. Here, we show how a sharp, discontinuous transition can occur, instead, as a generic feature of networks of phase oscillators. Precisely, we set conditions for the transition from unsynchronized to synchronized states to be first-order and demonstrate how these conditions can be attained in a very wide spectrum of situations. We then show how the occurrence of such transitions is always accompanied by the spontaneous setting of frequency-degree correlation features. Third, we show that the conditions for abrupt transitions can be even softened in several cases. Finally, we discuss, as a possible application, the use of this phenomenon to express magnetic-like states of synchronization.