Explosive transitions to synchronization in networks of phase oscillators (original) (raw)

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. M any complex systems operate transitions between different regimes or phases under the action of a control parameter. These transitions can be monitored using a global order parameter, a physical quantity (e.g. scalar, vector, …) accounting for the symmetry of the phases. Phase transitions can be of first or second order according to whether the order parameter varies continuously or discontinuously at a critical value of the control parameter. In complex networks theory 1 , phase transitions have been observed in the way the graph collectively organizes its architecture (e.g. percolation 2,3 ) and dynamical state (e.g. synchronization 4-6 ).