Kuramoto-like model of noisy oscillators

Abstract: The Kuramoto model is a paradigm to describe the dynamics of nonlinear oscillators under the influence of external perturbations or couplings. It is based on the idea to reduce the state equations to a scalar differential equation, that defines the time evolution for the phase of the oscillator. In this paper we discuss the reduction procedure for nonlinear oscillators subject to stochastic perturbations. The result is that phase noise is a drift-diffusion process. It is shown that the unavoidable amplitude fluctuations do change the expected frequency, and the frequency shift depends on the amplitude variance. The theoretical results are illustrated with the help of an example.