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

## 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 |
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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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