Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions

The mean field Kuramoto model describing the synchronization of a population of phase oscillators with a bimodal frequency distribution is analyzed (by the method of multiple scales) near regions in its phase diagram corresponding to synchronization to phases with a time-periodic order parameter. The richest behavior is found near the tricritical point where the incoherent, stationarily synchronized, "traveling wave" and "standing wave" phases coexist. The behavior near the tricritical point can be extrapolated to the rest of the phase diagram. Direct Brownian simulation of the model confirms our findings.