Holling's ''hungry mantid'' model for the invertebrate functional response considered as a Markov process. I: The full model and some of its limits
type: Item
instance of: scholarly article
title: Holling's ''hungry mantid'' model for the invertebrate functional response considered as a Markov process. I: The full model and some of its limits
zbMATH Open document ID: 0616.92008
DOI: 10.1007/BF00275716
author: F. H. D. van Batenburg
author: J. A. J. Metz
published in: Journal of Mathematical Biology
publication date: 1985-01-01T00:00:00Z
review text: In this paper we give an analytical reformulation of \textit{C. S. Holling}'s [Mem. Ent. Soc. Can. 48 (1966)] simulation model for invertebrate predatory behaviour. To this end we represent a population of predators as a frequency distribution over a space of (physiological) states. The functional response of a predator is calculated from the (stable) equilibrium distribution of its state as a function of prey density. Starting from the general model various other models are obtained by limit processes, some of them new and some of them old. The more interesting of which will be studied in further papers in this series.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 3999728
zbMATH Keywords: structured population models
zbMATH Keywords: van Kampen expansion
zbMATH Keywords: Holling's hungry mantid model
zbMATH Keywords: approximation by Markov processes
zbMATH Keywords: invertebrate predatory behaviour
zbMATH Keywords: frequency distribution
zbMATH Keywords: functional response
zbMATH Keywords: equilibrium distribution
zbMATH Keywords: limit processes
Wikidata QID: Q113909301
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3999728