Heteroclinic bifurcation in the Michaelis-Menten-type ratio-dependent predator-prey system

Bingtuan Li, Yang Kuang

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

The existence of a heteroclinic bifurcation for the Michaelis-Menten-type ratio dependent predator-prey system is rigorously established. Limit cycles related to the heteroclinic bifurcation are also discussed. It is shown that the heteroclinic bifurcation is characterized by the collision of a stable limit cycle with the origin, and the bifurcation triggers a catastrophic shift from the state of large oscillations of predator and prey populations to the state of extinction of both populations. It is also shown that the limit cycles related to the heteroclinic bifurcation originally bifurcate from the Hopf bifurcation.

Original languageEnglish (US)
Pages (from-to)1453-1464
Number of pages12
JournalSIAM Journal on Applied Mathematics
Volume67
Issue number5
DOIs
StatePublished - 2007

Fingerprint

Predator prey systems
Ratio-dependent
Hopf bifurcation
Bifurcation (mathematics)
Predator-prey System
Bifurcation
Limit Cycle
Predator
Prey
Trigger
Extinction
Hopf Bifurcation
Collision
Oscillation

Keywords

  • Bifurcation
  • Heteroclinic cycle
  • Ratio-dependent predator-prey model

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Heteroclinic bifurcation in the Michaelis-Menten-type ratio-dependent predator-prey system. / Li, Bingtuan; Kuang, Yang.

In: SIAM Journal on Applied Mathematics, Vol. 67, No. 5, 2007, p. 1453-1464.

Research output: Contribution to journalArticle

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