Bistable boundary conditions implying codimension 2 bifurcations
We consider generic families Xθ of smooth dynamical systems depending on parameters θ ∈ P where P is a 2-dimensional simply connected domain and assume that each Xθ 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 bifurcatio...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:20.500.14342/5202 |
| Acceso en línea: | http://hdl.handle.net/20.500.14342/5202 https://doi.org/10.1088/1361-6544/adb5e9 |
| Access Level: | acceso abierto |
| Palabra clave: | Dynamical systems Bifurcations Catastrophes Cusp bifurcation Bogdanov-Takens bifurcation Dinàmica Bifurcació, Teoria de la Catàstrofes (Matemàtica) 51 |
| Sumario: | We consider generic families Xθ of smooth dynamical systems depending on parameters θ ∈ P where P is a 2-dimensional simply connected domain and assume that each Xθ 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, there is a set of bifurcation curves in P that contain an odd number of cusps. In particular, there is at least one codimension 2 bifurcation point in the interior of P. |
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