Mutual Entrainment between Populations of Coupled Oscillators

Collective oscillations in a system of multiple populations of limit-cycle oscillators are studied. The oscillators are identical in each population, and besides their mutual coupling they are subject to noise. By means of a perturbation method, it is shown that a pair of populations with different collective frequencies is shown to exhibit synchronized/independent collective oscillations when the strength of their mutual coupling is sufficiently large/small. Furthermore, numerical simulations reveal a complicated bifurcation structure. We also study a system of four populations arranged in a ring. It is shown that the two populations which are coupled only indirectly can synchronize without entraining the intervening populations.