Computing the heteroclinic bifurcation curves in predator-prey systems with ratio-dependent functional response

Shigui Ruan, Yilei Tang, Weinian Zhang

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Predator-prey models with Michaelis-Menten-Holling type ratio- dependent functional response exhibit very rich and complex dynamical behavior, such as the existence of degenerate equilibria, appearance of limit cycles and heteroclinic loops, and the coexistence of two attractive equilibria. In this paper, we study heteroclinic bifurcations of such a predator-prey model. We first calculate the higher order Melnikov functions by transforming the model into a Hamiltonian system and then provide an algorithm for computing higher order approximations of the heteroclinic bifurcation curves.

Original languageEnglish (US)
Pages (from-to)223-241
Number of pages19
JournalJournal of Mathematical Biology
Volume57
Issue number2
DOIs
StatePublished - Aug 2008

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Predator prey systems
Ratio-dependent
Bifurcation Curve
Functional Response
Predator-prey System
Predator-prey Model
Melnikov Function
predators
Higher Order Approximation
Computing
Dynamical Behavior
Coexistence
Limit Cycle
Hamiltonian Systems
Hamiltonians
Bifurcation
Higher Order
Calculate
Model

Keywords

  • Approximation
  • Beta functions
  • Hamiltonian system
  • Heteroclinic loop
  • Melnikov functions
  • Predator-prey system

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

Computing the heteroclinic bifurcation curves in predator-prey systems with ratio-dependent functional response. / Ruan, Shigui; Tang, Yilei; Zhang, Weinian.

In: Journal of Mathematical Biology, Vol. 57, No. 2, 08.2008, p. 223-241.

Research output: Contribution to journalArticle

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