Periodic Orbits Bifurcating from a Nonisolated Zero-Hopf Equilibrium of Three-Dimensional Differential Systems Revisited

Murilo R. Cândido, Jaume Llibre

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1 Citation (Scopus)

Abstract

© 2018 World Scientific Publishing Company. In this paper, we study the periodic solutions bifurcating from a nonisolated zero-Hopf equilibrium in a polynomial differential system of degree two in ℝ3. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero-Hopf equilibrium. This new result is applied for studying the periodic solutions of differential systems in ℝ3 having n-scroll chaotic attractors.
Original languageEnglish
Article number1850058
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume28
Issue number5
DOIs
Publication statusPublished - 1 May 2018

Keywords

  • Averaging theory
  • periodic solutions
  • polynomial differential systems
  • zero-Hopf bifurcation
  • zero-Hopf equilibrium

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