Global dynamics of a predator-prey model with Hassell-Varley type functional response

Sze Bi Hsu, Tzy Wei Hwang, Yang Kuang

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

Predator-prey models with Hassell-Varley type functional response are appropriate for interactions where predators form groups and have applications in biological control. Here we present a systematic global qualitative analysis to a general predator-prey model with Hassell-Varley type functional response. We show that the predator free equilibrium is a global attractor only when the predator death rate is greater than its growth ability. The positive equilibrium exists if the above relation reverses. In cases of practical interest, we show that the local stability of the positive steady state implies its global stability with respect to positive solutions. For terrestrial predators that form a fixed number of tight groups, we show that the existence of an unstable positive equilibrium in the predator-prey model implies the existence of an unique nontrivial positive limit cycle.

Original languageEnglish (US)
Pages (from-to)857-871
Number of pages15
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume10
Issue number4
StatePublished - Nov 1 2008

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Keywords

  • Extinction
  • Functional response
  • Global stability
  • Limit cycles
  • Predator-prey model

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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