  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.
