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.
Publication Title
Physical Review Research
Volume
3
Issue
1
ISSN
26431564
DOI
10.1103/PhysRevResearch.3.013013
Comments
Published in the Physical Review Research under Open Access terms.