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Simple models of cannibalism : a critique and a new approach

Diekmann, O. and Nisbet, R.M. and Gurney, William and van den Bosch, F. (1986) Simple models of cannibalism : a critique and a new approach. Mathematical Biosciences, 78 (1). pp. 21-46. ISSN 0025-5564

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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.

Item type: Article
ID code: 41643
Keywords: cannibalism, egg cannibalism, Hopf bifurcation, scalar equation, Probabilities. Mathematical statistics, Agricultural and Biological Sciences(all), Biochemistry, Genetics and Molecular Biology(all), Modelling and Simulation, Applied Mathematics, Statistics and Probability, Immunology and Microbiology(all), Medicine(all)
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 23 Oct 2012 13:59
    Last modified: 05 Sep 2014 18:25
    URI: http://strathprints.strath.ac.uk/id/eprint/41643

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