Synchronization for the Rough Kuramoto Model
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915909550997504 |
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| author | Neamtu, Alexandra Blessing Kuehn, Christian Landi, Giacomo Rudik, Dennis |
| author_facet | Neamtu, Alexandra Blessing Kuehn, Christian Landi, Giacomo Rudik, Dennis |
| contents | We study the local synchronization of phases and frequencies for the Kuramoto model driven by rough noise. In particular, we prove exponential convergence towards synchronization and we give the explicit rate of convergence and quantify the size of the random basin of attraction. Furthermore, we show that the long time behavior of the system is determined by the evolution of phases' mean. Our result relies on the use of a Lyapunov function, capable of overriding the particular structure of the noise, taking in account only its intensity. Finally, we illustrate our analytical results and possible extensions with the help of numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02044 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Synchronization for the Rough Kuramoto Model Neamtu, Alexandra Blessing Kuehn, Christian Landi, Giacomo Rudik, Dennis Dynamical Systems Probability We study the local synchronization of phases and frequencies for the Kuramoto model driven by rough noise. In particular, we prove exponential convergence towards synchronization and we give the explicit rate of convergence and quantify the size of the random basin of attraction. Furthermore, we show that the long time behavior of the system is determined by the evolution of phases' mean. Our result relies on the use of a Lyapunov function, capable of overriding the particular structure of the noise, taking in account only its intensity. Finally, we illustrate our analytical results and possible extensions with the help of numerical simulations. |
| title | Synchronization for the Rough Kuramoto Model |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2604.02044 |