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Zero-Hopf Bifurcation in a Generalized Genesio Differential Equation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Zouhair Diab & Juan L. G. Guirao & Juan A. Vera, 2021. "Zero-Hopf Bifurcation in a Generalized Genesio Differential Equation," Mathematics, MDPI, vol. 9(4), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:354-:d:497251
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