Kuramoto model on the $D$-dimensional torus
Adaptation and Self-Organizing Systems
2026-05-05 v1
Abstract
We propose a generalization of the Kuramoto model of interacting oscillators in which the particles move on the surface of a -dimensional torus. In contrast with the traditional one-dimensional version, this model has a first order phase transition. We establish its mean field dynamics by means of a multidimensional Ott-Antonsen ansatz, and show that synchronization arises from a saddle-node bifurcation, while the incoherent state is always stable. Our theoretical calculations are validated by numerical simulations.
Cite
@article{arxiv.2605.01021,
title = {Kuramoto model on the $D$-dimensional torus},
author = {Marcel Novaes},
journal= {arXiv preprint arXiv:2605.01021},
year = {2026}
}
Comments
16 pages, 2 figures