On nonlinear dynamics of predator-prey models with discrete delay

Research output: Contribution to journalArticle

95 Scopus citations

Abstract

In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey models, generalized Gause-type predator-prey models with harvesting, etc. Bogdanov-Takens bifurcations in delayed predator-prey models with nonmonotone functional response and in delayed predator-prey model with predator harvesting are also introduced.

Original languageEnglish (US)
Pages (from-to)140-188
Number of pages49
JournalMathematical Modelling of Natural Phenomena
Volume4
Issue number2
DOIs
StatePublished - Jan 2009

Keywords

  • bifurcation
  • harvesting
  • predator-prey model
  • stability
  • time delay

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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