Etude d'un modèle de dynamique des populations

Details Etude d'un modèle de dynamique des populations Etude d'un modèle de dynamique des populations

2012-04-03

arxiv.org/abs/1204.0799v1

Mathematics

Dynamical Systems

This report (written in French) is a master 2 thesis made at University Paris-Sud (Orsay) in September 2004. Since December 20

Scientific paper

We study an infinite dimensional dynamical system that was proposed by J.C. Yoccoz and N.G. Yoccoz for modeling the population dynamics of some small rodents. We show an attractor exist in a large domain of the parameter space. Thanks to simulations, we describe the possible dynamics of the system, in particular some Henon-type strange attractors, but also a new kind of attractor. We study the complexity of the new attractor and the reasons causing it, from both geometrical and dynamical points of view. Thus, we show a chaotic behaviour can be obtained in a population dynamics model with a strong density-dependence and some delay, but without seasonal variations over years.

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