Ott-Antonsen reduction for the non-Abelian Kuramoto model on the 3-sphere

TL;DR

This paper extends the Ott-Antonsen reduction technique to a non-Abelian Kuramoto model on the 3-sphere, enabling low-dimensional analysis of coupled generalized oscillators.

Contribution

It introduces an Ott-Antonsen type reduction for the non-Abelian Kuramoto model on the 3-sphere, a novel extension for analyzing complex oscillator ensembles.

Findings

Derived low-dimensional dynamics for the non-Abelian Kuramoto model.

Extended Ott-Antonsen reduction to non-Abelian oscillator systems.

Facilitated analytical study of synchronization phenomena.

Abstract

We are interested in low-dimensional dynamics in an ensemble of coupled nonidentical generalized oscillators on the 3-sphere. The system of governing equations for such an ensemble is referred to as non-Abelian Kuramoto model in the literature. We establish an analogue (or an extension) of the Ott-Antonsen (OA) result for this model.