On the Equivalence of Synchronization Definitions in the Kuramoto Flow: A Unified Approach
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913168863789056 |
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| author | Hsiao, Ting-Yang Lo, Yun-Feng Zhu, Chengbin |
| author_facet | Hsiao, Ting-Yang Lo, Yun-Feng Zhu, Chengbin |
| contents | We present a rigorous mathematical framework establishing the equivalence of four classical notions of synchronization full phase-locking, phase-locking, frequency synchronization, and order parameter synchronization in generalized Kuramoto models, via a non-perturbative, finite-dimensional analysis. Our approach avoids linearization, mean-field limits, and restrictions on initial conditions, relying instead on global phase-space geometry, periodic vector field structure, and compactness arguments based on contradiction. These results clarify the foundational role of the order parameter and provide a unified understanding of synchronization across a broad class of heterogeneous oscillator networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19781 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Equivalence of Synchronization Definitions in the Kuramoto Flow: A Unified Approach Hsiao, Ting-Yang Lo, Yun-Feng Zhu, Chengbin Dynamical Systems 34D06, 34C15 We present a rigorous mathematical framework establishing the equivalence of four classical notions of synchronization full phase-locking, phase-locking, frequency synchronization, and order parameter synchronization in generalized Kuramoto models, via a non-perturbative, finite-dimensional analysis. Our approach avoids linearization, mean-field limits, and restrictions on initial conditions, relying instead on global phase-space geometry, periodic vector field structure, and compactness arguments based on contradiction. These results clarify the foundational role of the order parameter and provide a unified understanding of synchronization across a broad class of heterogeneous oscillator networks. |
| title | On the Equivalence of Synchronization Definitions in the Kuramoto Flow: A Unified Approach |
| topic | Dynamical Systems 34D06, 34C15 |
| url | https://arxiv.org/abs/2503.19781 |