Synchronization of Nonidentical Coupled Phase Oscillators in the Presence of Time Delay and Noise

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We have studied in this paper the dynamics of globally coupled phase oscillators having the Lorentzian frequency distribution with zero mean in the presence of both time delay and noise. Noise may be Gaussian or non-Gaussian in characteristics. In the limit of zero noise strength, we find that the critical coupling strength (CCS) increases linearly as a function of time delay. Thus the role of time delay in the dynamics for the deterministic system is qualitatively equivalent to the effect of frequency fluctuations of the phase oscillators by additive white noise in absence of time delay. But for the stochastic model, the critical coupling strength grows nonlinearly with the increase of the time delay. The linear dependence of the critical coupling strength on the noise intensity also changes to become nonlinear due to creation of additional phase difference among the oscillators by the time delay. We find that the creation of phase difference plays an important role in the dynamics of the system when the intrinsic correlation induced by the finite correlation time of the noise is small. We also find that the critical coupling is higher for the non-Gaussian noise compared to the Gaussian one due to higher effective noise strength.