Dynamics of coupled oscillator systems in the presence of a local potential

¹ Complex Systems and Theoretical Physics Unit, Health and Technology Department, Istituto Superiore di Sanità, and INFN Roma1 - Viale Regina Elena 299, 00161 Roma, Italy
² Max Planck Institute for the Physics of Complex Systems - Nöthnitzer Straße 38, 01187 Dresden, Germany

Received: 12 October 2016
Accepted: 30 November 2016

Abstract

We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in the presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective synchronization. We demonstrate by exact results and numerics a surprisingly rich long-time behavior, in which the system settles either into a stationary state that could be in or out of equilibrium and supports either global synchrony or absence of it, or in a time-periodic synchronized state. The system shows both continuous and discontinuous phase transitions, as well as an interesting reentrant transition in which the system successively loses and gains synchrony on steady increase of the relevant tuning parameter.