Synchronization in a System of Globally Coupled Oscillators with Time Delay

TL;DR

This paper investigates how time delay affects synchronization in globally coupled oscillators, revealing complex phase transitions, multistability, and suppression of synchronization frequency through analytical and numerical methods.

Contribution

It derives self-consistency equations incorporating delay effects and maps the phase diagram, highlighting novel discontinuous transitions and multistability phenomena.

Findings

Discontinuous and continuous synchronization transitions identified.

Multistability of coherent states with different frequencies.

Delay can suppress synchronization frequency.

Abstract

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition, between the incoherent state and a multitude of coherent states with different synchronization frequencies. In particular, the phase diagram is obtained on the plane of the coupling strength and the delay time, and ubiquity of multistability as well as suppression of the synchronization frequency is manifested. Numerical simulations are also performed to give consistent results.