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

Abstract

We consider the Kuramoto model of globally coupled phase oscillators with time-delayed interactions, that is subject to Ornstein–Uhlenbeck (Gaussian) colored or non-Gaussian colored noise. We investigate numerically the interplay between the influences of the finite correlation time of noise τ and the time delay τd on the onset of the synchronization process. The cases for identical and nonidentical oscillators have both 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 τ. 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 have 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 detail and presented results for possible cases of colored Gaussian and non-Gaussian noises.

Mean square H<inf>&#x2212;</inf> synchronization of coupled nonlinear delay stochastic partial differential systems

“…If we take P = 10 −3 I, then Q = (10 −9 + 10 −12 )I, it is not difficult to verify the inequalities (4). Therefore, systems (14) achieve the mean square asymptotical synchronization.…”

“…Usually, the bandwidth of communication channel is bounded, time-delay is inevitable when the data needed to be transmitted is large. Time-delay also can destroy the synchronization [4][5][6]. The synchronization of stochastic delay systems is well considered [7][8][9][10][11].…”

Synchronization of Kuramoto Oscillators with Distance-dependent Delay

“…The stability of incoherence in such a model has been studied by Yeung and Strogatz in [8] and by others [9][10][11]. However, in most situations, the delays are not all identical.…”

Synchronization in a network of delay coupled maps with stochastically switching topologies

“…Delay can enhance the coherence of chaotic motion 21 , as well as it can stabilize synchronous state in oscillator network 22 . Some new phenomena like oscillation death, stabilizing periodic orbits, enhancement or suppression of synchronization, chimera state etc arise due to the time delay [23][24][25][26][27][28] . So there are strong reasons to shed light on the issue of such systems.…”