Etude d'un mod\`ele de dynamique des populations
Abstract
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.
Cite
@article{arxiv.1204.0799,
title = {Etude d'un mod\`ele de dynamique des populations},
author = {Sylvain Arlot},
journal= {arXiv preprint arXiv:1204.0799},
year = {2012}
}
Comments
This report (written in French) is a master 2 thesis made at University Paris-Sud (Orsay) in September 2004. Since December 2004, this report was available as a preprint of the Mathematics laboratory of University Paris-Sud (preprint number 2004-38), as well as on the author's webpage. Compared to the original version of the report, some graphics have been compressed (with some information loss). The complete report with original graphics is available on the author's webpage http://www.di.ens.fr/~arlot/dea.htm