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 Scopus citations

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 1 2008

Keywords

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

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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