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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.12246 |
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| _version_ | 1866909476494245888 |
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| author | Rand, David A Saez, Meritxell |
| author_facet | Rand, David A Saez, Meritxell |
| contents | We consider generic families $X_\param$ of smooth dynamical systems depending on parameters $\param\in P$ where $P$ is a 2-dimensional simply connected domain and assume that each $X_\param$ only has a finite number of restpoints and periodic orbits. We prove that if over the boundary of $P$ there is a S or Z shaped bifurcation graph containing two opposing fold bifurcation points while over the rest of the boundary there are no other bifurcation points, then, if there is no fold-Hopf bifurcation in $P$ then there is at least one cusp in the interior of $P$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12246 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bistable boundary conditions implying codimension 2 bifurcations Rand, David A Saez, Meritxell Dynamical Systems 37G35 We consider generic families $X_\param$ of smooth dynamical systems depending on parameters $\param\in P$ where $P$ is a 2-dimensional simply connected domain and assume that each $X_\param$ only has a finite number of restpoints and periodic orbits. We prove that if over the boundary of $P$ there is a S or Z shaped bifurcation graph containing two opposing fold bifurcation points while over the rest of the boundary there are no other bifurcation points, then, if there is no fold-Hopf bifurcation in $P$ then there is at least one cusp in the interior of $P$. |
| title | Bistable boundary conditions implying codimension 2 bifurcations |
| topic | Dynamical Systems 37G35 |
| url | https://arxiv.org/abs/2309.12246 |