Transversal conics and the existence of limit cycles
This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré-Bendixson regions by using transversal conics. We present several examples of known systems in the literature showing diferent featur...
| Authors: | , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Universitat de Lleida (UdL) |
| Repository: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/49434 |
| Online Access: | https://doi.org/10.1016/j.jmaa.2015.03.015 http://hdl.handle.net/10459.1/49434 |
| Access Level: | Open access |
| Keyword: | Transversal conic Poincaré–Bendixson region Limit cycle Planar differential system |
| Summary: | This paper deals with the problem of location and existence of limit cycles for real planar polynomial differential systems. We provide a method to construct Poincaré-Bendixson regions by using transversal conics. We present several examples of known systems in the literature showing diferent features about limit cycles: hyperbolicity, Hopf bifurcation, sky-blue bifurcation, rotated vector fields, . . . for which the obtained Poincaré-Bendixson region allows to locate the limit cycles. Our method gives bounds for the bifurcation values of parametrical families of planar vector fields and intervals of existence of limit cycles. |
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