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...

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Detalles Bibliográficos
Autores: Giacomini, Héctor, Grau Montaña, Maite
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/49434
Acceso en línea:https://doi.org/10.1016/j.jmaa.2015.03.015
http://hdl.handle.net/10459.1/49434
Access Level:acceso abierto
Palabra clave:Transversal conic
Poincaré–Bendixson region
Limit cycle
Planar differential system
Descripción
Sumario: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.