Noise effects on synchronization in systems of coupled oscillators

We study the synchronization phenomena in systems of globally coupled oscillators, each possessing finite inertia, with particular attention to the noise effects. The self-consistency equation for the order parameter as well as the probability distribution is obtained from the Smoluchowski equation, and analyzed in the presence of thermal noise. It is found that the hysteresis present in the system without noise disappears as the thermal noise comes into the system. Numerical simulations are also performed to give results generally consistent with the analytical ones.