Inertia perturbation theory for the inertial Kuramoto model
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912539161395200 |
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| author | Cho, Hangjun Dong, Jiu-Gang Ha, Seung-Yeal Ryoo, Seung-Yeon |
| author_facet | Cho, Hangjun Dong, Jiu-Gang Ha, Seung-Yeal Ryoo, Seung-Yeon |
| contents | In this work, we study the inertial Kuramoto model, which is a second-order extension of the classical first-order Kuramoto model, as an inertial perturbation of the first-order Kuramoto model. We develop a quantitative Tikhonov theorem, from which we derive a new synchronization statement in the small inertia regime, with strong bounds on the limiting order parameter. We also explore the determinability of phase velocities from phase positions, which shows that the perturbation viewpoint must be limited to the small inertia regime. This paper complements our recent work (2025), where we established asymptotic phase-locking of inertial Kuramoto oscillators under generic initial conditions in the low inertia-high coupling regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inertia perturbation theory for the inertial Kuramoto model Cho, Hangjun Dong, Jiu-Gang Ha, Seung-Yeal Ryoo, Seung-Yeon Dynamical Systems Mathematical Physics Classical Analysis and ODEs 34E15 (Primary) 34D06, 34C15, 82C22 (Secondary) In this work, we study the inertial Kuramoto model, which is a second-order extension of the classical first-order Kuramoto model, as an inertial perturbation of the first-order Kuramoto model. We develop a quantitative Tikhonov theorem, from which we derive a new synchronization statement in the small inertia regime, with strong bounds on the limiting order parameter. We also explore the determinability of phase velocities from phase positions, which shows that the perturbation viewpoint must be limited to the small inertia regime. This paper complements our recent work (2025), where we established asymptotic phase-locking of inertial Kuramoto oscillators under generic initial conditions in the low inertia-high coupling regime. |
| title | Inertia perturbation theory for the inertial Kuramoto model |
| topic | Dynamical Systems Mathematical Physics Classical Analysis and ODEs 34E15 (Primary) 34D06, 34C15, 82C22 (Secondary) |
| url | https://arxiv.org/abs/2508.11241 |