Dynamics of coupled oscillator systems in presence of a local potential

TL;DR

This paper investigates a long-range coupled oscillator model with a local potential and thermal noise, revealing complex long-term behaviors including various phase transitions and synchronization phenomena.

Contribution

It introduces a generalized oscillator model extending the Kuramoto framework, demonstrating exact results and numerical analysis of its rich dynamical phases.

Findings

Presence of both stationary and time-periodic synchronized states

Observation of continuous and discontinuous phase transitions

Identification of reentrant transition behavior

Abstract

We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in 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 into either 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.