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We consider the Kuramoto model of globally coupled phase oscillators withtime-delayed interactions, that is subject to the Ornstein-Uhlenbeck (Gaussian)colored or the non-Gaussian colored noise. We investigate numerically theinterplay between the influences of the finite correlation time of noise $\tau$and the time delay $\tau_{d}$ on the onset of the synchronization process. Bothcases for identical and nonidentical oscillators had been considered. Among theobtained results for identical oscillators is a large increase of thesynchronization threshold as a function of time delay for the colorednon-Gaussian noise compared to the case of the colored Gaussian noise at lownoise correlation time $\tau$. However, the difference reduces remarkably forlarge noise correlation times. For the case of nonidentical oscillators, theincoherent state may become unstable around the maximum value of the threshold(as a function of time delay) even at lower coupling strength values in thepresence of colored noise as compared to the noiseless case. We had studied thedependence of the critical value of the coupling strength (the threshold ofsynchronization) on given parameters of the stochastic Kuramoto model in greatdetails and presented results for possible cases of colored Gaussian andnon-Gaussian noises.

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