Cycles in cannibalistic egg-larval interactions
type: Item
instance of: scholarly article
title: Cycles in cannibalistic egg-larval interactions
zbMATH Open document ID: 0608.92014
DOI: 10.1007/BF00275508
author: Alan Hastings
published in: Journal of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: This is a well written paper which deals with a population dynamics model affected by cannibalistic effects and inspired by the biological behavior of Tribolium. Making the assumption that the interaction between cannibalistic larvae and eggs is described by a linear functional response, the model is described by a system of two integral equations being of the form studied by \textit{O. Diekmann} and \textit{S. A. van Gils} [J. Differ. Equations 54, 139-180 (1984; Zbl 0543.45004)]. It is observed here that with an appropriate choice of the parameters a stable equilibrium point and a stable periodic solution are simultaneously performed. Finally, several tables with numerical results are presented by varying the parameters.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45M99
Mathematics Subject Classification ID: 45M10
zbMATH DE Number: 3985027
zbMATH Keywords: cannibalistic egg-larval interactions
zbMATH Keywords: cycles
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: nonlinear Volterra integral equations
zbMATH Keywords: local stability properties
zbMATH Keywords: attractors
zbMATH Keywords: population dynamics model
zbMATH Keywords: Tribolium
zbMATH Keywords: linear functional response
zbMATH Keywords: stable equilibrium point
zbMATH Keywords: stable periodic solution
zbMATH Keywords: numerical results
reviewed by: George Karakostas
MaRDI profile type: Publication
Wikidata QID: Q113909309
cites work: Invariant manifolds for Volterra integral equations of convolution type
cites work: Simple mathematical models for cannibalism: A critique and a new approach
cites work: Some simple models of cannibalism
cites work: On Populations that Cannibalize Their Young
description: scientific article; zbMATH DE number 3985027