Codimension two bifurcations in a predator-prey system with group defense

Dongmei Xiao, Shigui Ruan

Research output: Contribution to journalArticle

32 Scopus citations


In this paper we study the qualitative behavior of a predator-prey system with nonmonotonic functional response. The system undergoes a series of bifurcations including the saddle-node bifurcation, the supercritical Hopf bifurcation, and the homoclinic bifurcation. For different parameter values the system could have a limit cycle or a homoclinic loop, or exhibit the so-called "paradox of enrichment" phenomenon. In the generic case, the model has the bifurcation of cusp-type codimension two (i.e. the Bogdanov-Takens bifurcation) but no bifurcations of codimension three.

Original languageEnglish (US)
Pages (from-to)2123-2131
Number of pages9
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number8
StatePublished - 2001
Externally publishedYes


ASJC Scopus subject areas

  • General
  • Applied Mathematics

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