Versal unfoldings of predator-prey systems with ratio-dependent functional response

Shigui Ruan, Yilei Tang, Weinian Zhang

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


In this paper we study the versal unfolding of a predator-prey system with ratio-dependent functional response near a degenerate equilibrium in order to obtain all possible phase portraits for its perturbations. We first construct the unfolding and prove its versality and degeneracy of codimension 2. Then we discuss all its possible bifurcations, including transcritical bifurcation, Hopf bifurcation, and heteroclinic bifurcation, give conditions of parameters for the appearance of closed orbits and heteroclinic loops, and describe the bifurcation curves. Phase portraits for all possible cases are presented.

Original languageEnglish (US)
Pages (from-to)1410-1435
Number of pages26
JournalJournal of Differential Equations
Issue number6
StatePublished - Sep 2010


  • Bifurcation
  • Degenerate equilibrium
  • Heteroclinic loop
  • Normal form
  • Predator-prey system
  • Versal unfolding

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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