Scopus: 11 citas, Google Scholar: citas
Bifurcation values for a familiy of planar vector fields of degree five
García Saldaña, Johanna Denise (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Giacomini, Hector (Université de Tours (France). Laboratoire de Mathématiques et Physique Théorique)

Fecha: 2015
Resumen: We study the number of limit cycles and the bifurcation diagram in the Poincar' sphere of a one-parameter family of planar differential equations of degree e ˙ five x = Xb (x) which has been already considered in previous papers. We prove that there is a value b∗ > 0 such that the limit cycle exists only when b ∈ (0, b∗ ) and that it is unique and hyperbolic by using a rational Dulac function. Moreover we provide an interval of length 27/1000 where b∗ lies. As far as we know the tools used to determine this interval are new and are based on the construction of algebraic curves without contact for the flow of the differential equation. These curves are obtained using analytic information about the separatrices of the infinite critical points of the vector field. To prove that the Bendixson-Dulac Theorem works we develop a method for studying whether one-parameter families of polynomials in two variables do not vanish based on the computation of the so called double discriminant.
Nota: Número d'acord de subvenció MCYT/MTM2008-03437
Nota: Número d'acord de subvenció CIRIT/2009/SGR-410
Derechos: Tots els drets reservats.
Lengua: Anglès
Documento: article ; recerca ; acceptedVersion
Materia: Bifurcation ; Double discriminant ; Dulac function ; Phase portrait on the Poincaré sphere ; Polynomial planar system ; Uniqueness of limit cycles
Publicado en: Discrete and continuous dynamical systems. Series A, Vol. 35 Núm. 2 (2015) , p. 669-701, ISSN 1553-5231

DOI: 10.3934/dcds.2015.35.669


Postprint
33 p, 1.1 MB

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Documentos de investigación > Documentos de los grupos de investigación de la UAB > Centros y grupos de investigación (producción científica) > Ciencias > GSD (Grupo de sistemas dinámicos)
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 Registro creado el 2016-01-12, última modificación el 2020-11-01



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