Etude d'un mod\`ele de dynamique des populations

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.