Dynamics of two populations of phase oscillators with different frequency distributions

A large variety of rhythms are observed in nature. Rhythms such as electroencephalogram signals in the brain can often be regarded as interacting. In this study, we investigate the dynamical properties of rhythmic systems in two populations of phase oscillators with different frequency distributions. We assume that the average frequency ratio between two populations closely approximates some small integer. Most importantly, we adopt a specific coupling function derived from phase reduction theory. Under some additional assumptions, the system of two populations of coupled phase oscillators reduces to a low-dimensional system in the continuum limit. Consequently, we find chimera states in which clustering and incoherent states coexist. Finally, we confirm consistent behaviors of the derived low-dimensional model and the original model.