Analyse mathématique et simulations d'un modèle prédateur-proie en milieu insulaire hétérogène

Abstract : The aim of this thesis is to develop and analyse deterministic predator-prey models for species living in heterogeneous insular environments. We are interested in the evolution of a native prey population, after the introduction of alien species, predators and competitors. In a first part we look at the spatially unstructured models; this yields singular systems of ODEs, some denominator of the RHS can be zero. The mathematical analysis gives some conditions for persistence or finite time extinction of populations. The asymptotical behaviour depends on additional hypotheses. In a similar way, we study the case of a native prey species split into 2 age stages: juveniles and adults. The second part deals with spatial models. We derive models taking into account the spatial heterogeneities of the environment and their effects on demographic parameters. We use reaction-diffusion systems with a singular logistic right hand side. Detailed analysis of these models gives criteria for global existence versus finite time existence of the solutions. At the same time, we develop a well adapted numerical method, using splitting methods, to validate the spatial models and allow the study of invasion processes. Numerical results point out the essential role played by the introduced prey population in successful invasion of isolated native preys colonies by the predator species. Finally, the discrete age structure for the native species allows us to exhibit oscillatory behaviours.
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Liste complète des métadonnées
Contributor : Sébastien Gaucel <>
Submitted on : Thursday, March 13, 2008 - 3:01:41 PM
Last modification on : Thursday, January 11, 2018 - 6:21:22 AM
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  • HAL Id : tel-00263910, version 1



Sébastien Gaucel. Analyse mathématique et simulations d'un modèle prédateur-proie en milieu insulaire hétérogène. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 2005. Français. 〈tel-00263910〉



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