Hétérogénéité spatiale en dynamique des populations

Abstract : The purpose of this thesis is the mathematical and numerical study of a system of several species competing for a single resource in a heterogeneous environment. When the environment is homogeneous, it is known that such a system, called chemostat system, satisfies the so-called competitive exclusion principle: no more than one species can survive. We propose two spatially structured models and study the role of spatial heterogeneity in the coexistence phenomena. The first model is a system of matrix equations, the second one is a reaction-diffusion system. Our first contribution is to show that the solutions of the reaction-diffusion system are uniformly bounded in time and space in L infinity norm. Next, we study the case of small migration rate in the discrete model and show that the coexistence of several species is possible. Lastly, in the case of high migration rates, we use the center manifold theorem to show in each of the two models that the principle of competitive exclusion holds. Then, we construct stationary coexistence solutions for two species using a method of global bifurcations. This construction leads to the identification of a coexistence domain in the parameter space. In the final chapters, we illustrate and extend numerically the previous results. In particular, we show how the coexistence domain depends on the migration rate and on the spatial heterogeneity.
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Submitted on : Thursday, June 16, 2011 - 5:17:27 PM
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  • HAL Id : tel-00600942, version 2

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Sten Madec. Hétérogénéité spatiale en dynamique des populations. Mathématiques [math]. Université Rennes 1, 2011. Français. ⟨tel-00600942v2⟩

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