Low-Dimensional Reduction Theory for Populations of Globally Coupled Phase Oscillators with Multiharmonic Coupling: A Method Based on OPUC Theory

Low-dimensional reduction theories, such as the Ott-Antonsen ansatz, have played a crucial role in the study of populations of globally coupled phase oscillators. However, most of these theories are applicable only to models in which the interaction is described by a single harmonic component, limiting their application to more realistic oscillator models. In this paper, by employing the theory of orthogonal polynomials on the unit circle (OPUC), we construct a framework that enables low-dimensional reduction for populations of globally coupled phase oscillators with multiharmonic coupling.