Collective dynamics of coupled modulated oscillators with random pinning

Abstract We present a study of a large pool of coupled oscillators in the presence of a modulated external field. Random distributed pinning phases introduce a disordering element. We find that phase locking of the oscillator community to the harmonics of the frequency of the applied field always is associated with a complete loss of coherence between the oscillators. The phase-lock regions form islands in parameter space, the size of which decreases for increasing coupling strength to vanish completely at a critical value. By stability considerations the shape of the phase-locked islands is reduced to a two points boundary problem of a first order non-autonomous differential equation and an approximation is found for high frequencies. The structure of the coherent states is discussed and a first order approximation is found in the limit of strong coherence.