Frequency-locking of coupled oscillators driven by periodic forces and white noise

•Dynamics of coupled oscillators driven by periodic force and white noise was investigated.•Rotation numbers of all oscillators were proved to be the same.•Frequency-locking of oscillators was shown to be robust to noise perturbation.•Bell-shaped dependence of the rotation number on the coupling strength was shown.

This paper presents a theoretical analysis on frequency-locking of N coupled oscillators driven by both periodic forces and white noise. The difficulty is that the considered system is time-inhomogeneous and thus no stationary distribution exists. Technically, by considering a set of stationary Markov processes subtracted from the original non-stationary process, we prove that for any given coupling strength K>0K>0, all the coupled oscillators have the same rotation number in L2L2 sense. Furthermore, some interesting numerical results are presented, such as the benefit of noise on accelerating the rotation number, a bell-shaped dependence of the rotation number on the coupling strength, and the robust of the synchronization to noise perturbation.