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.