Hopf periodic orbits for a ratio-dependent predator-prey model with stage structure

Jaume Llibre, Claudio Vidal

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1 Citation (Scopus)

Abstract

A ratio-dependent predator-prey model with stage structure for prey was investigated in [8]. There the authors mentioned that they were unable to show if such a model admits limit cycles when the unique equilibrium point E∗ at the positive octant is unstable. Here we characterize the existence of Hopf bifurcations for the systems. In particular we provide a positive answer to the above question showing for such models the existence of small-amplitude Hopf limit cycles being the equilibrium point E∗ unstable.
Original languageEnglish
Pages (from-to)1859-1867
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume21
Issue number6
DOIs
Publication statusPublished - 1 Aug 2016

Keywords

  • Averaging theory
  • Hopf bifurcation
  • Predator-prey model
  • Ratio-dependence

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