Abstract
We study a phase oscillator network on a circle with an infinite-range interaction. First, we treat the Mexican-hat interaction with the zeroth and first Fourier components. We give detailed derivations of the auxiliary equations for the phases and self-consistent equations for the amplitudes. We solve these equations and characterize the nontrivial solutions in terms of order parameters and the rotation number. Furthermore, we derive the boundaries of the bistable regions and study the bifurcation structures in detail. Expressions for location-dependent resultant frequencies and entrained phases are also derived. Secondly, we treat a different interaction that is composed of mth and nth Fourier components, where m<n, and we study its nontrivial solutions. In both cases, the results of numerical simulations agree quite well with the theoretical results.
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