Sufficient conditions for the existence of periodic solutions of the extended Duffing–Van der Pol oscillator

In this paper, some aspects on the periodic solutions of the extended Duffing–Van der Pol oscillator are discussed. Doing different rescaling of the variables and parameters of the system associated with the extended Duffing–Van der Pol oscillator, we show that it can bifurcate one or three periodic...

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Detalles Bibliográficos
Autores: Euzébio, Rodrigo D. [UNESP], Llibre, Jaume
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/171875
Acceso en línea:http://dx.doi.org/10.1080/00207160.2015.1046847
http://hdl.handle.net/11449/171875
Access Level:acceso abierto
Palabra clave:averaging theory
extended Duffing–Van der Pol oscillator
non-autonomous systems
periodic solution
Descripción
Sumario:In this paper, some aspects on the periodic solutions of the extended Duffing–Van der Pol oscillator are discussed. Doing different rescaling of the variables and parameters of the system associated with the extended Duffing–Van der Pol oscillator, we show that it can bifurcate one or three periodic solutions from a two-dimensional manifold filled by periodic solutions of the referred system. For each rescaling we exhibit concrete values for which these bounds are reached. Beyond that we characterize the stability of some periodic solutions. Our approach is analytical and the results are obtained using the averaging theory and some algebraic techniques.