Zero-hopf bifurcation in the volterra-gause system of predator-prey type

Jean Marc Ginoux, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


© 2017 John Wiley & Sons, Ltd. We prove that the Volterra-Gause system of predator-prey type exhibits 2 kinds of zero-Hopf bifurcations for convenient values of their parameters. In the first, 1 periodic solution bifurcates from a zero-Hopf equilibrium, and in the second, 4 periodic solutions bifurcate from another zero-Hopf equilibrium. This study is done using the averaging theory of second order.
Original languageEnglish
Pages (from-to)7858-7866
JournalMathematical Methods in the Applied Sciences
Issue number18
Publication statusPublished - 1 Dec 2017


  • Periodic orbits
  • Predator-prey system
  • Volterra-Gause system
  • Zero-Hopf bifurcation


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