Predator-prey models with delay and prey harvesting

Annik Martin, Shigui Ruan

Research output: Contribution to journalArticle

147 Scopus citations

Abstract

It is known that predator-prey systems with constant rate harvesting exhibit very rich dynamics. On the other hand, incorporating time delays into predator-prey models could induce instability and bifurcation. In this paper we are interested in studying the combined effects of the harvesting rate and the time delay on the dynamics of the generalized Gause-type predator-prey models and the Wangersky-Cunningham model. It is shown that in these models the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities, while the harvesting rate has a stabilizing effect on the equilibrium if it is under the critical harvesting level. In particular, one of these models loses stability when the delay varies and then regains its stability when the harvesting rate is increased. Computer simulations are carried to explain the mathematical conclusions.

Original languageEnglish (US)
Pages (from-to)247-267
Number of pages21
JournalJournal of Mathematical Biology
Volume43
Issue number3
DOIs
StatePublished - Sep 2001
Externally publishedYes

Keywords

  • Bifurcation
  • Harvesting
  • Predator-prey
  • Stability
  • Time delay

ASJC Scopus subject areas

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

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