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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Bibliographic Details
Authors: Euzébio, R.|||0000-0001-8083-5216, Llibre, Jaume|||0000-0002-9511-5999
Format: article
Publication Date:2016
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:221043
Online Access:https://ddd.uab.cat/record/221043
https://dx.doi.org/urn:doi:10.1080/00207160.2015.1046847
Access Level:Open access
Keyword:Extended Duffing-Van der Pol oscillator
Periodic solution
Non-autonomous systems
Averaging theory
Description
Summary: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.