Coexistence of Analytic and Piecewise Analytic Limit Cycles in Planar Piecewise Quadratic Differential Systems
We study the simultaneous bifurcation of limit cycles in planar piecewise quadratic differential systems separated by a straight line. These limit cycles arise from a degenerate Hopf bifurcation at two equilibrium points in the positive and negative half-planes, as well as from an equilibrium on the...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:312571 |
| Acceso en línea: | https://ddd.uab.cat/record/312571 https://dx.doi.org/urn:doi:10.1007/s12346-025-01252-8 |
| Access Level: | acceso abierto |
| Palabra clave: | Piecewise quadratic vector fields Limit cycles Simultaneous bifurcation Degenerate Hopf bifurcation |
| Sumario: | We study the simultaneous bifurcation of limit cycles in planar piecewise quadratic differential systems separated by a straight line. These limit cycles arise from a degenerate Hopf bifurcation at two equilibrium points in the positive and negative half-planes, as well as from an equilibrium on the separation line. All the limit cycles are of small amplitude. This bifurcation creates a configuration of limit cycles of type (3,5,3). Additionally, in each half-plane, the maximum number of small-amplitude hyperbolic limit cycles that a quadratic vector field can have is three. |
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