I will briefly explain how one usually models synchronization of coupled phase oscillators, first in the case of two coupled oscillators, and then for the Kuramoto model of a large number of oscillators with all-to-all coupling. Then I will outline some recent results, obtained with Georgi Medvedev and Gideon Simpson (Drexel University, Philadelphia) on the effect of noise on a model of oscillators on the discrete circle with nearest neighbour coupling. In the deterministic case, the stable and unstable equilibrium configurations of this system are well understood. In addition, the system has a gradient structure, which allows the application of techniques from stochastic analysis (large deviations, potential theory) to quantify the metastable transitions in the presence of weak noise.
