Limit cycles of discontinuous piecewise polynomial vector fields

When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x= -y((x^2 y^2)/2)^m and y= x((x^2 y^2)/2)^m with m 1, when we perturb it inside a class of discontinuous piecewise polynomial vector fie...

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Detalles Bibliográficos
Autores: de Carvalho, Tiago, Llibre, Jaume|||0000-0002-9511-5999, Tonon, Durval José.|||0000-0002-2733-1825
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:182510
Acceso en línea:https://ddd.uab.cat/record/182510
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2016.11.048
Access Level:acceso abierto
Palabra clave:Averaging theory
Limit cycles
Piecewise smooth vector fields
Descripción
Sumario:When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x= -y((x^2 y^2)/2)^m and y= x((x^2 y^2)/2)^m with m 1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields.