Geodesic
Predator-Prey Interactions, Age Structures and Delay Equations
M. Mohr1 ; M. V. Barbarossa2 ; C. Kuttler3
1 University of Heidelberg, Institute of Applied Mathematics, D-69120 Heidelberg, Germany
2 Bolyai Institute, University of Szeged, H-6720 Szeged, Hungary
3 Institute of Mathematics, Technische Universität München, D-85748 Garching, Germany
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 1, pp. 92-107.

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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.
DOI : 10.1051/mmnp/20149107

M. Mohr 1 ; M. V. Barbarossa 2 ; C. Kuttler 3

1 University of Heidelberg, Institute of Applied Mathematics, D-69120 Heidelberg, Germany
2 Bolyai Institute, University of Szeged, H-6720 Szeged, Hungary
3 Institute of Mathematics, Technische Universität München, D-85748 Garching, Germany 
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M. Mohr; M. V. Barbarossa; C. Kuttler. Predator-Prey Interactions, Age Structures and Delay Equations. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 1, pp. 92-107. doi : 10.1051/mmnp/20149107. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149107/

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