Zero-Hopf bifurcation in the generalized Michelson system

Jaume Llibre, Amar Makhlouf

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)


© 2015 Elsevier Ltd We provide sufficient conditions for the existence of two periodic solutions bifurcating from a zero–Hopf equilibrium for the differential systemx˙=y,y˙=z,z˙=a+by+cz−x2/2,where a, b and c are real arbitrary parameters. The regular perturbation of this differential system provides the normal form of the so–called triple–zero bifurcation.
Original languageEnglish
Pages (from-to)228-231
JournalChaos, Solitons and Fractals
Publication statusPublished - 1 Aug 2016


  • Averaging theory
  • Michelson system
  • Periodic solution
  • Triple-zero bifurcation
  • Zero–Hopf Bifurcation


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