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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.20541 |
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Table of Contents:
- Zhang and Strogatz [Phys. Rev. Lett. 127, 194101 (2021)] used high-dimensional simulations to argue that basins of attraction in the Kuramoto ring are octopus-like: their volume scales as $e^{-kq^2}$ in the winding number $q$, nearly all of it concentrated in filamentary tentacles rather than near the attractor. They conjecture this geometry to be common in high dimensions but note that high-dimensional simulations are unreliable. We prove every feature of the octopus picture rigorously for identical oscillators on a ring coupled by any smooth odd function strictly increasing on $(-π,π)$.