On the Dynamics of Predator-Prey Models with the Beddington-DeAngelis Functional Response

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240 Scopus citations

Abstract

The dynamics of predator-prey models with the Beddington-DeAngelis functional response are analyzed, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type 2 functional response but contains an extra term describing mutual interference by predators. Both spatially homogeneous models based on ordinary differential equations and reaction-diffusion models are considered. Criteria for permanence and for predator extinction are derived. For systems without diffusion or with no-flux boundary conditions, criteria are derived for the existence of a globally stable coexistence equilibrium or, alternatively, for the existence of periodic orbits.

Original languageEnglish (US)
Pages (from-to)206-222
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume257
Issue number1
DOIs
StatePublished - May 1 2001

Keywords

  • Predator-prey; reaction-diffusion; functional response; permanence; uniform persistence

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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