Spontaneous synchronisation and nonequilibrium statistical mechanics of coupled phase oscillators

Year: 2018

Authors: Gherardini Stefano; Gupta Shamik; Ruffo Stefano

Autors Affiliation: Department of Physics, University of Florence, via S. Marta 3, I-50139 Florence, INFN and LENS, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy; Department of Physics, Ramakrishna Mission Vivekananda University, Belur Math, Howrah 711202, India; SISSA, via Bonomea 265, CNISM and INFN, I-34136 Trieste, Italy.

Abstract: Spontaneous synchronisation is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously exhibit collective oscillations at a common frequency. The Kuramoto model provides the basic analytical framework to study spontaneous synchronisation. The model comprises limit-cycle oscillators with distributed natural frequencies interacting through a mean-field coupling. Although more than forty years have passed since its introduction, the model continues to occupy the centre stage of research in the field of non-linear dynamics and is also widely applied to model diverse physical situations. In this brief review, starting with a derivation of the Kuramoto model and the synchronisation phenomenon it exhibits, we summarise recent results on the study of a generalised Kuramoto model that includes inertial effects and stochastic noise. We describe the dynamics of the generalised model from a different yet a rather useful perspective, namely, that of long-range interacting systems driven out of equilibrium by quenched disordered external torques. A system is said to be long-range interacting if the inter-particle potential decays slowly as a function of distance. Using tools of statistical physics, we highlight the equilibrium and nonequilibrium aspects of the dynamics of the generalised Kuramoto model, and uncover a rather rich and complex phase diagram that it exhibits, which underlines the basic theme of intriguing emergent phenomena that are exhibited by many-body complex systems.

Journal/Review: CONTEMPORARY PHYSICS

Volume: 59 (3)      Pages from: 229  to: 250

KeyWords: Synchronisation, statistical physics, nonequilibrium stationary state, phase transition
DOI: 10.1080/00107514.2018.1464100

Citations: 9
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