Algebraic limit cycles bifurcating from algebraic ovals of quadratic centers

In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles. In this paper, we study quadratic polynomial systems with an algebraic periodic...

Descripción completa

Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Tian, Yun
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221283
Acceso en línea:https://ddd.uab.cat/record/221283
https://dx.doi.org/urn:doi:10.1142/S0218127418501456
Access Level:acceso abierto
Palabra clave:Quadratic systems
Quadratic vector fields
Quadratic center
Periodic orbit
Limit cycle
Bifurcation from center
Cyclicity of the period annulus
Descripción
Sumario:In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles. In this paper, we study quadratic polynomial systems with an algebraic periodic orbit of degree 4 surrounding a center. We show that there exists only one family of such systems satisfying that an algebraic limit cycle of degree 4 can bifurcate from the period annulus of the mentioned center under quadratic perturbations.