Transcritical and zero-Hopf bifurcations in the Genesio system

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 equati...

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Detalles Bibliográficos
Autores: Cardin, Pedro Toniol|||0000-0002-8723-8200, 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:182513
Acceso en línea:https://ddd.uab.cat/record/182513
https://dx.doi.org/urn:doi:10.1007/s11071-016-3259-2
Access Level:acceso abierto
Palabra clave:Averaging theory
Genesio system
Transcritical bifurcation
Zero--Hopf bifurcation
Descripción
Sumario: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