Periodic synchronization in a driven system of coupled oscillators

We study dynamic responses of a set of globally coupled oscillators with randomly distributed frequencies, which is, in the absence of external driving, known to exhibit a transition between the incoherent state and the coherent one with spontaneous synchronization. When each oscillator is driven by periodic force, it displays the characteristic mode locking known as Shapiro steps. Under periodic driving of randomly distributed strengths, the system as a whole is shown to exhibit periodic synchronization as well as transitions between the coherent and the incoherent states. The detailed behavior depends on the characteristic strength of driving relative to the driving frequency.