On a stable torus in a 3D system with a saddle-focus
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911444765769728 |
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| author | Shilnikov, Andrey L. Shilnikov answered Leonid P. |
| author_facet | Shilnikov, Andrey L. Shilnikov answered Leonid P. |
| contents | This paper proposes a conceptual model for the onset of a stable torus near a saddle-focus equilibrium. This bifurcation scenario is typical of slow-fast systems that generate elliptic bursting in a variety of neuronal models in mathematical neuroscience. Variants of the model also capture other dynamical regimes recurring in a neighborhood of the saddle-focus. We also discuss homoclinic bifurcations for which the model assumptions are feasible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12451 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a stable torus in a 3D system with a saddle-focus Shilnikov, Andrey L. Shilnikov answered Leonid P. Dynamical Systems This paper proposes a conceptual model for the onset of a stable torus near a saddle-focus equilibrium. This bifurcation scenario is typical of slow-fast systems that generate elliptic bursting in a variety of neuronal models in mathematical neuroscience. Variants of the model also capture other dynamical regimes recurring in a neighborhood of the saddle-focus. We also discuss homoclinic bifurcations for which the model assumptions are feasible. |
| title | On a stable torus in a 3D system with a saddle-focus |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2602.12451 |