Zero-Hopf Bifurcation in a Generalized Genesio Differential Equation

Zouhair Diab, Juan L. G. Guirao and Juan A. Vera
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Zouhair Diab: Zouhair Diab Department of Mathematics and Computer Science, Larbi Tebessi University, Tebessa 12002, Algeria
Juan L. G. Guirao: Departamento de Matemáca Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Región de Murcia, Spain
Juan A. Vera: Centro Universitario de la Defensa, Academia General del Aire, Universidad Politécnica de Cartagena, 30720 Santiago de la Ribera, Región de Murcia, Spain

Mathematics, 2021, vol. 9, issue 4, 1-11

Abstract: The purpose of the present paper is to study the presence of bifurcations of zero-Hopf type at a generalized Genesio differential equation. More precisely, by transforming such differential equation in a first-order differential system in the three-dimensional space R 3 , we are able to prove the existence of a zero-Hopf bifurcation from which periodic trajectories appear close to the equilibrium point located at the origin when the parameters a and c are zero and b is positive.

Keywords: Zero-Hopf bifurcation; periodic solutions; ordinary differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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