Degenerate Fold-Hopf Bifurcations in a Rössler-Type System

G. Tigan, J. Llibre, L. Ciurdariu

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3 Citations (Scopus)


© 2017 World Scientific Publishing Company. We study the Hopf and the fold-Hopf bifurcations of the Rössler-type differential system [Equation presented here], with b≠0. We show that the classical Hopf bifurcation cannot be applied to this system for detecting the fold-Hopf bifurcation, which here is studied using the averaging theory. Our results show that a Hopf bifurcation takes place at the equilibrium (-ac/b,c/b,c/b) when c = a < 0. This Hopf bifurcation becomes a fold-Hopf bifurcation when c = a = 0.
Original languageEnglish
Article number1750068
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number5
Publication statusPublished - 1 May 2017


  • Rössler system
  • averaging theory
  • fold-Hopf bifurcation
  • periodic orbits
  • zero-Hopf bifurcation


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