Global dynamics of a ratio-dependent predator-prey system

Dongmei Xiao, Shigui Ruan

Research output: Contribution to journalArticle

205 Scopus citations

Abstract

Recently, ratio-dependent predator-prey systems have been regarded by some researchers to be more appropriate for predator-prey interactions where predation involves serious searching processes. However, such models have set up a challenging issue regarding their dynamics near the origin since these models are not well-defined there. In this paper, the qualitative behavior of a class of ratio-dependent predator-prey system at the origin in the interior of the first quadrant is studied. It is shown that the origin is indeed a critical point of higher order. There can exist numerous kinds of topological structures in a neighborhood of the origin including the parabolic orbits, the elliptic orbits, the hyperbolic orbits, and any combination of them. These structures have important implications for the global behavior of the model. Global qualitative analysis of the model depending on all parameters is carried out, and conditions of existence and non-existence of limit cycles for the model are given. Computer simulations are presented to illustrate the conclusions.

Original languageEnglish (US)
Pages (from-to)268-290
Number of pages23
JournalJournal of Mathematical Biology
Volume43
Issue number3
DOIs
StatePublished - Sep 2001
Externally publishedYes

Keywords

  • Attractor
  • Critical point of higher order
  • Limit cycle
  • Predator-prey system
  • Ratio-dependent response

ASJC Scopus subject areas

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

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