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

Jaume Llibre, Ammar Makhlouf

Research output: Contribution to journalArticleResearch

2 Citations (Scopus)

Abstract

© 2017, Foundation for Scientific Research and Technological Innovation. We study the zero-Hopf bifurcation of the third-order differential equations x″′+(a1x+a0)x″+(b1x+b0)x′+x2=0,where a, a 1 , b and b 1 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.
Original languageEnglish
Pages (from-to)75-82
JournalDifferential Equations and Dynamical Systems
Volume27
DOIs
Publication statusPublished - 15 Jan 2019

Keywords

  • Averaging theory
  • Periodic orbit
  • Quadratic system
  • Third-order differential equation

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