Lifetime of the incoherent state of coupled phase oscillators

In this paper we have studied the relaxation of the incoherent state to the coherent state of coupled phase oscillators with time delay in terms of lifetime of the incoherent state both in the presence and absence of noise. To make the present study general we have considered both Gaussian and non Gaussian noises. Our investigation shows that the mean lifetime (MLT) decreases exponentially as the coupling strength among the oscillators grows. It also shows that MLT changes non monotonically with an increase in time delay. Another observation is that the mean lifetime increases exponentially as a function of noise strength for white noise. However, for colour noise, it grows linearly with an increase in noise strength. Enhancement of the correlation time of the coloured noise suppresses MLT. The rate of suppression is faster for non-Gaussian noise compared to the Gaussian case. Finally, we have observed that the mean lifetime increases exponentially as the noise behaviour deviates more from the Gaussian characteristics