Centers and limit cycles of polynomial differential systems of degree 4 via averaging theory

In this paper we classify the phase portraits in the Poincar\'e disc of the centers of the generalized class of Kukles systems \[ =-y,=x ax^3y bxy^3, \] symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the pe...

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Detalles Bibliográficos
Autores: Benterki, Rebiha|||0000-0001-6745-2747, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169499
Acceso en línea:https://ddd.uab.cat/record/169499
https://dx.doi.org/urn:doi:10.1016/j.cam.2016.08.047
Access Level:acceso abierto
Palabra clave:Averaging method
Center
Generalized Kukles system
Limit cycle
Phase portrait
Descripción
Sumario:In this paper we classify the phase portraits in the Poincar\'e disc of the centers of the generalized class of Kukles systems \[ =-y,=x ax^3y bxy^3, \] symmetric with respect to the y-axis, and we study, using the averaging theory up to sixth order, the limit cycles which bifurcate from the periodic solutions of these centers when we perturb them inside the class of all polynomial differential systems of degree 4.