Phase holonomy underlies puzzling temporal patterns in Kuramoto models with two sub-populations

TL;DR

This paper uncovers how geometric phase, a concept from physics, explains complex behaviors like chimeras and traveling waves in Kuramoto models with two sub-populations, revealing a novel underlying mechanism.

Contribution

It introduces the concept of geometric phase as a fundamental explanation for dynamical patterns in Kuramoto models, a novel perspective in this context.

Findings

Chimeras and traveling waves are linked to geometric phase emergence.

First identification of geometric phase phenomena in Kuramoto oscillator ensembles.

Provides a geometric framework for understanding complex synchronization patterns.

Abstract

We present a geometric investigation of curious dynamical behaviors previously reported in Kuramoto models with two sub-populations. Our study demonstrates that chimeras and traveling waves in such models are associated with the birth of geometric phase. Although manifestations of geometric phase are frequent in various fields of Physics, this is the first time (to our best knowledge) that such a phenomenon is exposed in ensembles of Kuramoto oscillators or, more broadly, in complex systems.