Math. Model. Nat. Phenom.
Volume 9, Number 1, 2014Issue dedicated to Michael Mackey
|Page(s)||92 - 107|
|Published online||07 February 2014|
Predator-Prey Interactions, Age Structures and Delay Equations
1 University of Heidelberg, Institute
of Applied Mathematics, D-69120
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:
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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