Critical threshold for synchronizability of high-dimensional Kuramoto oscillators under higher-order interactions

Hyungjin Huh; Dohyun Kim

doi:10.1063/5.0211410

Critical threshold for synchronizability of high-dimensional Kuramoto oscillators under higher-order interactions

Chaos. 2024 Dec 1;34(12):123119. doi: 10.1063/5.0211410.

Authors

Hyungjin Huh¹, Dohyun Kim²

Affiliations

¹ Department of Mathematics, Chung-Ang University, Seoul 06974, Republic of Korea.
² Department of Mathematics Education, Sungkyunkwan University, Seoul 03063, Republic of Korea.

PMID: 39625672
DOI: 10.1063/5.0211410

Abstract

We study the asymptotic dynamics of the high-dimensional Kuramoto oscillators on the unit sphere with two- and three-body interactions that trigger competition between synchrony and non-synchrony. In this work, we find a critical threshold between interaction strengths for complete synchronizability. Moreover, critical slowing down is observed at this phase transition. Our main theorems are supplemented by several numerical experiments, which provide a qualitative insight beyond theoretical results.