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Predator-Prey Interactions, Age Structures and Delay Equations

Published online by Cambridge University Press:  07 February 2014

M. Mohr ,
M. V. Barbarossa  and
C. Kuttler
M. Mohr*
Affiliation:
University of Heidelberg, Institute of Applied Mathematics, D-69120 Heidelberg, Germany
M. V. Barbarossa
Affiliation:
Bolyai Institute, University of Szeged, H-6720 Szeged, Hungary
C. Kuttler
Affiliation:
Institute of Mathematics, Technische Universität München, D-85748 Garching, Germany
*
⋆ Corresponding author. E-mail: marcel.mohr@bioquant.uni-heidelberg.de
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Abstract

A general framework for age-structured predator-prey systems is introduced. Individuals are distinguished into two classes, juveniles and adults, and several possible interactions are considered. The initial system of partial differential equations is reduced to a system of (neutral) delay differential equations with one or two delays. Thanks to this approach, physically correct models for predator-prey with delay are provided. Previous models are considered and analysed in view of the above results. A Rosenzweig-MacArthur model with delay is presented as an example.

Keywords

predator-preyage structurepopulation dynamicsdelay differential equationsneutral equationsRosenzweig-MacArthur model
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 1: Issue dedicated to Michael Mackey , 2014 , pp. 92 - 107
Copyright
© EDP Sciences, 2014

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