Kuramoto model on the $D$-dimensional torus

Marcel Novaes

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arXiv · 2605.01021

Kuramoto model on the $D$-dimensional torus

Marcel Novaes

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Abstract

We propose a generalization of the Kuramoto model of interacting oscillators in which the particles move on the surface of a $D$-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.

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Marcel Novaes. 2026-05-01. Kuramoto model on the $D$-dimensional torus. https://arxiv.org/abs/2605.01021

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