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Modélisation mathématique structurée en taille du zooplancton

Jonathan Rault 1 
1 BIOCORE - Biological control of artificial ecosystems
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique
Abstract : The aim of this thesis is the formulation and the study of some prey-predator models to describe phytoplankton and zooplankton population dynamics, with size-structure of the zooplankton. This study was mainly motivaded by the data collected by the Laboratoire d'Oceanographie de Villefranche-Sur-Mer, and especially the evolution since 1966 of the zooplankton size-spectra. In a first part we show data and build different models with either a continuous size-structure, leading to a partial differential equation coupled to an ordinary differential equation, or a discrete structure corresponding to different develop- ment stages and leading to a system of ordinary differential equations. A mathematical study is done for some particular cases of these models (equilibria and their stability, stabilization of an equilibrium using a positive control). Cannibalism being common in zooplankton community, we also study it, particularly in a two stages model. We show that cannibalism can stabilize the dynamics or even can be an evolutionary stable strategy. Finally we try to compare numerically models to data and observe some qualitative similarities
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Submitted on : Monday, August 12, 2013 - 3:35:42 PM
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  • HAL Id : tel-00850906, version 1

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Jonathan Rault. Modélisation mathématique structurée en taille du zooplancton. Mathématiques générales [math.GM]. Université Nice Sophia Antipolis, 2012. Français. ⟨tel-00850906⟩

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