Title

Spectrum of extensive multiclusters in the Kuramoto model with higher-order interactions

Document Type

Article

Department

​Mathematics

Publication Date

1-7-2021

Abstract

Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., nonadditive, higher-order interactions between three or more units) continues to grow, we study an extension of the Kuramoto model where oscillators are coupled via three-way interactions that exhibits novel dynamical properties including clustering, multistability, and abrupt desynchronization transitions. Here we provide a rigorous description of the stability of various multicluster states by studying their spectral properties in the thermodynamic limit. Not unlike the classical Kuramoto model, a natural frequency distribution with infinite support yields a population of drifting oscillators, which in turn guarantees that a portion of the spectrum is located on the imaginary axes, resulting in neutrally stable or unstable solutions. On the other hand, a natural frequency distribution with finite support allows for a fully phase-locked state, whose spectrum is real and may be linearly stable or unstable.

Comments

Published in the Physical Review Research under Open Access terms.

Publication Title

Physical Review Research

Volume

3

Issue

1

ISSN

26431564

DOI

10.1103/PhysRevResearch.3.013013

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