Simple models of cannibalism: a critique and a new approach

O. Diekmann, R.M. Nisbet, William Gurney, F. van den Bosch

Research output: Contribution to journalArticle

71 Citations (Scopus)

Abstract

We show how to incorporate a functional response in recent models of Gurtin, Levine, and others for egg cannibalism. Starting from a relatively complicated model with vulnerability spread over an age interval of finite duration ϵ, we arrive at a much simpler model by passing to the limit ϵ ↓ 0. It turns out that survivorship through the vulnerable stage is implicitly determined by the solution of a scalar equation. Subsequently we study the existence and stability of steady states, and we find (analytically in a simple case, numerically in more general situations) curves in a two-dimensional parameter space where a nontrivial steady state loses its stability and a periodic solution arises through a Hopf bifurcation.
Original languageEnglish
Pages (from-to)21-46
Number of pages26
JournalMathematical Biosciences
Volume78
Issue number1
DOIs
Publication statusPublished - 31 Mar 1986

Keywords

  • cannibalism
  • egg cannibalism
  • Hopf bifurcation
  • scalar equation

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