The Tentacles Landscape
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918461846847488 |
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| author | Groisman, Pablo |
| author_facet | Groisman, Pablo |
| 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 $(-π,π)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20541 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Tentacles Landscape Groisman, Pablo Mathematical Physics Dynamical Systems 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 $(-π,π)$. |
| title | The Tentacles Landscape |
| topic | Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2604.20541 |