Kuramoto model on the $D$-dimensional torus
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910184847179776 |
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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 |