| Abstract: |
| Collective synchronization in the Kuramoto model has been widely studied, but the original model is defined on the unit circle and only includes pairwise interactions. In this presentation, based on [Huh and Kim, Chaos (2024), 123119], we study a high-dimensional Kuramoto model with both two-body and three-body interactions. Let $\kappa_1$ and $\kappa_2$ denote the corresponding interaction strengths. We show that complete synchronization can emerge if $\kappa_1+\kappa_2>0$, whereas it cannot occur if $\kappa_1+\kappa_2\lt 0$. In the critical case $\kappa_1+\kappa_2=0$, the emergence of synchronization depends crucially on the sign of $\kappa_1$, and critical slowing down is observed at the threshold. Our analysis provides a rigorous characterization of the critical line suggested in [Kovalenko et al., Phys. Rev. Lett. (2021), 258301]. Numerical experiments complement the theory and reveal additional qualitative behaviors. |
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