We consider general properties of groups of interacting oscillators, for which the natural frequencies are not in resonance. Such groups interact via non-oscillating collective variables like the amplitudes of the order parameters defined for each group. We treat the phase dynamics of the groups using the Ott-Antonsen ansatz and reduce it to a system of coupled equations for the order parameters. We describe different regimes of co-synchrony in the groups. For a large number of groups, heteroclinic cycles, corresponding to a sequental synchronous activity of groups, and chaotic states, where the order parameters oscillate irregularly, are possible.
@article{arxiv.1102.1319,
title = {Effects of non-resonant interaction in ensembles of phase oscillators},
author = {Maxim Komarov and Arkady Pikovsky},
journal= {arXiv preprint arXiv:1102.1319},
year = {2015}
}