Effect of time delay on the onset of synchronization of the stochastic Kuramoto model

TL;DR

This paper investigates how time delay and colored noise influence the synchronization onset in the stochastic Kuramoto model, revealing significant effects of noise type and correlation time on synchronization thresholds.

Contribution

It provides a detailed numerical analysis of the interplay between time delay, noise correlation, and noise type in the stochastic Kuramoto model, including both identical and nonidentical oscillators.

Findings

Synchronization threshold increases with time delay under non-Gaussian noise.

Difference in thresholds between Gaussian and non-Gaussian noise diminishes at large correlation times.

Colored noise can destabilize incoherent states at lower coupling strengths.

Abstract

We consider the Kuramoto model of globally coupled phase oscillators with time-delayed interactions, that is subject to the Ornstein-Uhlenbeck (Gaussian) colored or the non-Gaussian colored noise. We investigate numerically the interplay between the influences of the finite correlation time of noise $\tau$ and the time delay $\tau_{d}$ on the onset of the synchronization process. Both cases for identical and nonidentical oscillators had been considered. Among the obtained results for identical oscillators is a large increase of the synchronization threshold as a function of time delay for the colored non-Gaussian noise compared to the case of the colored Gaussian noise at low noise correlation time $\tau$. However, the difference reduces remarkably for large noise correlation times. For the case of nonidentical oscillators, the incoherent state may become unstable around the maximum value of the threshold (as a function of time delay) even at lower coupling strength values in the presence of colored noise as compared to the noiseless case. We had studied the dependence of the critical value of the coupling strength (the threshold of synchronization) on given parameters of the stochastic Kuramoto model in great details and presented results for possible cases of colored Gaussian and non-Gaussian noises.