Bifurcation of Limit Cycles from a Fold-Fold Singularity in a Glacial Cycles Model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917057865449472 |
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| author | Makarenkov, Oleg Widiasih, Esther |
| author_facet | Makarenkov, Oleg Widiasih, Esther |
| contents | We study the occurrence of limit cycles from a point on the discontinuity hyperplane $L$ between two smooth vector fields where the two vector fields both point towards one another. Generically, such a point (called switched equilibrium in control) is asymptotically stable, but we consider the situation where the two vector fields become tangent to L at the switched equilibrium under varying parameter making a degenerate fold-fold singularity. We prove that moving the parameter past such a singular value leads to the occurrence of an attracting limit cycle, which is exactly the dynamical mechanism we then discover in a conceptual model of glacial cycles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_02143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bifurcation of Limit Cycles from a Fold-Fold Singularity in a Glacial Cycles Model Makarenkov, Oleg Widiasih, Esther Dynamical Systems 34A36, 37G15, 86A08 34A36, 37G15, 86A08 34A36, 37G15, 86A08 We study the occurrence of limit cycles from a point on the discontinuity hyperplane $L$ between two smooth vector fields where the two vector fields both point towards one another. Generically, such a point (called switched equilibrium in control) is asymptotically stable, but we consider the situation where the two vector fields become tangent to L at the switched equilibrium under varying parameter making a degenerate fold-fold singularity. We prove that moving the parameter past such a singular value leads to the occurrence of an attracting limit cycle, which is exactly the dynamical mechanism we then discover in a conceptual model of glacial cycles. |
| title | Bifurcation of Limit Cycles from a Fold-Fold Singularity in a Glacial Cycles Model |
| topic | Dynamical Systems 34A36, 37G15, 86A08 34A36, 37G15, 86A08 34A36, 37G15, 86A08 |
| url | https://arxiv.org/abs/2511.02143 |