Title: 4-dimensional zero-Hopf bifurcation for polynomial differentials systems with cubic homogeneous nonlinearities via averaging theory

Authors: Amina Feddaoui; Jaume Llibre; Amar Makhlouf

Addresses: Department of Mathematics, University of Annaba, Laboratory LMA, P.O. Box 12, Annaba 23000, Algeria ' Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain ' Department of Mathematics, University of Annaba, Laboratory LMA, P.O. Box 12, Annaba 23000, Algeria

Abstract: The averaging theory of second order shows that for polynomial differential systems in ℝ4 with cubic homogeneous nonlinearities at least nine limit cycles can be born in a zero-Hopf bifurcation.

Keywords: Hopf bifurcation; averaging theory; cubic polynomial differential systems.

DOI: 10.1504/IJDSDE.2020.109106

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.4, pp.321 - 328

Received: 30 Jul 2018
Accepted: 01 Dec 2018
Published online: 20 Aug 2020 *

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