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

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.