Synchrony for weak coupling in the complexified Kuramoto model
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916229990580224 |
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| author | Thümler, Moritz Srinivas, Shesha G. M. Schröder, Malte Timme, Marc |
| author_facet | Thümler, Moritz Srinivas, Shesha G. M. Schröder, Malte Timme, Marc |
| contents | We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the real-variable system. However, synchrony persists in the form of \textit{complex locked states} for coupling strengths $K$ below the transition $K^{(\text{pl})}$ to classical \textit{phase locking}. Stable complex locked states indicate a locked sub-population of zero mean frequency in the real-variable model and their imaginary parts help identifying which units comprise that sub-population. We uncover a second transition at $K'<K^{(\text{pl})}$ below which complex locked states become linearly unstable yet still exist for arbitrarily small coupling strengths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Synchrony for weak coupling in the complexified Kuramoto model Thümler, Moritz Srinivas, Shesha G. M. Schröder, Malte Timme, Marc Adaptation and Self-Organizing Systems We present the finite-size Kuramoto model analytically continued from real to complex variables and analyze its collective dynamics. For strong coupling, synchrony appears through locked states that constitute attractors, as for the real-variable system. However, synchrony persists in the form of \textit{complex locked states} for coupling strengths $K$ below the transition $K^{(\text{pl})}$ to classical \textit{phase locking}. Stable complex locked states indicate a locked sub-population of zero mean frequency in the real-variable model and their imaginary parts help identifying which units comprise that sub-population. We uncover a second transition at $K'<K^{(\text{pl})}$ below which complex locked states become linearly unstable yet still exist for arbitrarily small coupling strengths. |
| title | Synchrony for weak coupling in the complexified Kuramoto model |
| topic | Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2404.19637 |