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

Dongmei Xiao, Shigui Ruan

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

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
Volume11
Issue number8
DOIs
StatePublished - 2001
Externally publishedYes

Fingerprint

Predator prey systems
Bifurcation (mathematics)
Predator-prey System
Codimension
Bifurcation
Homoclinic Loop
Bogdanov-Takens Bifurcation
Homoclinic Bifurcation
Saddle-node Bifurcation
Hopf bifurcation
Functional Response
Qualitative Behavior
Cusp
Paradox
Limit Cycle
Hopf Bifurcation
Series
Model

ASJC Scopus subject areas

  • General
  • Applied Mathematics

Cite this

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AB - 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.

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