Glassy states and super-relaxation in populations of coupled phase oscillators

• Published in: Nature communications 2014-06, Vol.5 (1), p.4118-4118, Article 4118
• Main Authors: Iatsenko, D., McClintock, P.V.E., Stefanovska, A.
• Format: Article
• Language: English
• Subjects: 639/301/1034; Humanities and Social Sciences; multidisciplinary; Science; Science (multidisciplinary)
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/ncomms5118

Large networks of coupled oscillators appear in many branches of science, so that the kinds of phenomena they exhibit are not only of intrinsic interest but also of very wide importance. In 1975, Kuramoto proposed an analytically tractable model to describe these systems, which has since been successfully applied in many contexts and remains a subject of intensive research. Some related problems, however, remain unclarified for decades, such as the existence and properties of the oscillator glass state. Here we present a detailed analysis of a very general form of the Kuramoto model. In particular, we find the conditions when it can exhibit glassy behaviour, which represents a kind of synchronous disorder in the present case. Furthermore, we discover a new and intriguing phenomenon that we refer to as super-relaxation where the oscillators feel no interaction at all while relaxing to incoherence. Our findings offer the possibility of creating glassy states and observing super-relaxation in real systems. The Kuramoto model attempts to describe the behaviour and properties of networks of coupled oscillators. By studying a generalization of the original Kuramoto model, Latsenko et al. identify several previously unseen complex phenomena that can appear in such networks.