Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation

We study the zero-Hopf bifurcation of the third-order differential equations x″'+(a1x+a0)x″+(b1x+b0)x'+x2=0,where a, a , b and b are real parameters. The prime denotes derivative with respect to an independent variable t. We also provide an estimate of the zero-Hopf periodic solution and t...

Descripción completa

Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Makhlouf, Ammar
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:204386
Acceso en línea:https://ddd.uab.cat/record/204386
https://dx.doi.org/urn:doi:10.1007/s12591-017-0375-5
Access Level:acceso abierto
Palabra clave:Periodic orbit
Third-order differential equation
Quadratic system
Averaging theory
Descripción
Sumario:We study the zero-Hopf bifurcation of the third-order differential equations x″'+(a1x+a0)x″+(b1x+b0)x'+x2=0,where a, a , b and b are real parameters. The prime denotes derivative with respect to an independent variable t. We also provide an estimate of the zero-Hopf periodic solution and their kind of stability. The Hopf bifurcations of these differential systems were studied in [5], here we complete these studies adding their zero-Hopf bifurcations.