Transitions amongst synchronous solutions in the stochastic Kuramoto model

We consider the Kuramoto model of coupled oscillators with nearest-neighbour coupling and additive white noise. We show that synchronous solutions which are stable without the addition of noise become metastable and that we have transitions amongst synchronous solutions on long timescales. We compute these timescales and, moreover, compute the most likely path in phase space that transitions will follow. We show that these transition timescales do not increase as the number of oscillators in the system increases, and are roughly constant in the system size. Finally, we show that the transitions correspond to a splitting of one synchronous solution into two communities which move independently for some time and which rejoin to form a different synchronous solution.