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.
@article{arxiv.1212.0404,
title = {Explosive transitions to synchronization in networked phase oscillators},
author = {I. Leyva and I. Sendiña-Nadal and J. Almendral and A. Navas and M. Zanin and D. Papo and J. M. Buldú and S. Boccaletti},
journal= {arXiv preprint arXiv:1212.0404},
year = {2014}
}