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Journal of Mathematical Biology

, Volume 14, Issue 2, pp 231–250 | Cite as

A predator prey model with age structure

  • J. M. Cushing
  • M. Saleem
Article

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 periodm of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for smallm or are destabilized asm decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.

Key words

Predator-prey Age structure Stability 

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • J. M. Cushing
    • 1
  • M. Saleem
    • 1
  1. 1.Department of Mathematics and Program in Applied MathematicsUniversity of ArizonaTucsonUSA

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