### Abstract

Language | English |
---|---|

Pages | 21-46 |

Number of pages | 26 |

Journal | Mathematical Biosciences |

Volume | 78 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1986 |

### Fingerprint

### Keywords

- cannibalism
- egg cannibalism
- Hopf bifurcation
- scalar equation

### Cite this

*Mathematical Biosciences*,

*78*(1), 21-46. https://doi.org/10.1016/0025-5564(86)90029-5

}

*Mathematical Biosciences*, vol. 78, no. 1, pp. 21-46. https://doi.org/10.1016/0025-5564(86)90029-5

**Simple models of cannibalism : a critique and a new approach.** / Diekmann, O.; Nisbet, R.M.; Gurney, William; van den Bosch, F.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Simple models of cannibalism

T2 - Mathematical Biosciences

AU - Diekmann, O.

AU - Nisbet, R.M.

AU - Gurney, William

AU - van den Bosch, F.

PY - 1986/3

Y1 - 1986/3

N2 - 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.

AB - 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.

KW - cannibalism

KW - egg cannibalism

KW - Hopf bifurcation

KW - scalar equation

U2 - 10.1016/0025-5564(86)90029-5

DO - 10.1016/0025-5564(86)90029-5

M3 - Article

VL - 78

SP - 21

EP - 46

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 1

ER -