descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 27 Dec 2016 English Publisher:Springer Science and Business Media LLCJournal:Nonlinear Dynamics, volume 88, pages 547-553 (issn: 0924-090X, eissn: 1573-269X,

Authors: Pedro Toniol Cardin; Jaume Llibre;

doi: 10.1007/s11071-016-3259-2

handle: 11449/174011

Transcritical and zero-Hopf bifurcations in the Genesio system

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Abstract

Agraïments: The first author is supported by FAPESP Grant No. 2013/24541-0. Both authors are supported by CAPES Grant 88881.030454/2013-01 Program CSF-PVE. In this paper we study the existence of transcritical and zero--Hopf bifurcations of the third--order ordinary differential equation a b c x - x^2 = 0, called the Genesio equation, which has a unique quadratic nonlinear term and three real parameters. More precisely, writing this differential equation as a first order differential system in \R^3

Related Organizations

Universidade Estadual Paulista - UNESP
Brazil
Autonomous University of Barcelona
Spain
Sao Paulo State University
Brazil

Keywords

Zero--Hopf bifurcation, Zero-Hopf Bifurcation, Transcritical bifurcation, Averaging theory, 531, Genesio system

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