Dynamics of multifrequency oscillator communities

We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between the communities' frequencies are derived. The mostly simple situation of three resonantly interacting groups is analyzed in details. We find conditions for the mutual coupling to promote or suppress synchrony in individual populations, and present examples where interaction between communities leads to their synchrony, or to a partially asynchronous state, or to a chaotic dynamics of order parameters.