title: Explosive transitions to synchronization in networks of phase oscillators.
abstract: 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.
authors: Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.
authors: I
authors: I
authors: Leyva
authors: A
authors: A
authors: Navas
authors: I
authors: I
authors: Sendiña-Nadal
authors: J A
authors: JA
authors: Almendral
authors: J M
authors: JM
authors: Buldú
authors: M
authors: M
authors: Zanin
authors: D
authors: D
authors: Papo
authors: S
authors: S
authors: Boccaletti