| Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 1, 2014
Issue dedicated to Michael Mackey
|
|
|---|---|---|
| Page(s) | 92 - 107 | |
| DOI | https://doi.org/10.1051/mmnp/20149107 | |
| Published online | 07 February 2014 | |
Predator-Prey Interactions, Age Structures and Delay Equations
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
⋆ Corresponding author. E-mail:
marcel.mohr@bioquant.uni-heidelberg.de
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.
Mathematics Subject Classification: 92D25 / 34K17 / 34K40 / 34K20
Key words: predator-prey / age structure / population dynamics / delay differential equations / neutral equations / Rosenzweig-MacArthur model
© EDP Sciences, 2014
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