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 0025-5564Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|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|
|Depositing user:||Pure Administrator|
|Date Deposited:||23 Oct 2012 12:59|
|Last modified:||06 Aug 2016 00:13|