A predator prey model with age structure

J. M. Cushing, M. Saleem

Research output: Contribution to journalArticle

62 Scopus citations

Abstract

A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects its fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and destabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the maturation period m of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for small m or are destabilized as m decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.

Original languageEnglish (US)
Pages (from-to)231-250
Number of pages20
JournalJournal of mathematical biology
Volume14
Issue number2
DOIs
StatePublished - Jun 1982

Keywords

  • Age structure
  • Predator-prey
  • Stability

ASJC Scopus subject areas

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

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