Collective phenomena in large populations of globally coupled relaxation oscillators.

We present a study of a large pool of globally coupled relaxation oscillators. The reaction of the pool to the presence of a modulating external field is discussed. The coupling is assumed homogeneous and linear. Randomly distributed internal frequencies introduce a disordering element that, due to the coupling, can result in oscillator quiescence. Self-synchronization is shown to be absent in this system. However, this is entirely due to the linear coupling. For identical oscillators the basic state is incoherent and marginally stable in an extended region of parameter space. With modulation on the levels, the average rotation number as function of the external frequency lies on a devil's staircase, as for a single oscillator. However, the locked regions shrink with increasing coupling