Kuramoto model on the $D$-dimensional torus

Fuente: arXiv
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Auteur principal: Novaes, Marcel
Format: Preprint
Publié: 2026
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author Novaes, Marcel
author_facet Novaes, Marcel
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_01021
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Kuramoto model on the $D$-dimensional torus
Novaes, Marcel
Adaptation and Self-Organizing Systems
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.
title Kuramoto model on the $D$-dimensional torus
topic Adaptation and Self-Organizing Systems
url https://arxiv.org/abs/2605.01021