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

TL;DR

This paper introduces a new framework using OPUC theory to achieve low-dimensional reduction in populations of globally coupled phase oscillators with multiharmonic coupling, extending beyond single harmonic models.

Contribution

The authors develop a novel reduction method based on OPUC theory that applies to multiharmonic coupling in oscillator populations, surpassing previous single harmonic limitations.

Findings

Enables reduction for multiharmonic coupling models.

Extends applicability of low-dimensional theories.

Provides a new analytical tool for complex oscillator networks.

Abstract

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.