alpha-Kuramoto partitions: graph partitions from the frustrated Kuramoto model generalise equitable partitions

TL;DR

This paper explores how the alpha-Kuramoto model, which includes phase frustration, induces graph partitions and generalizes equitable partitions, providing theoretical insights and characterizations.

Contribution

It proves that all equitable partitions are alpha-Kuramoto partitions and offers an exact characterization of bipartitions within this framework.

Findings

Every equitable partition is an alpha-Kuramoto partition

Converse does not necessarily hold for all alpha-Kuramoto partitions

Provides an exact characterization of alpha-Kuramoto bipartitions

Abstract

The Kuramoto model describes the collective dynamics of a system of coupled oscillators. An alpha-Kuramoto partition is a graph partition induced by the Kuramoto model, when the oscillators include a phase frustration parameter. We prove that every equitable partition is an alpha-Kuramoto partition, but that the converse does necessarily not hold. We give an exact characterisation of alpha-Kuramoto bipartitions.