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.
Publié le : 2004-09-14
Classification:
Strange attractor,
chaotic dynamic,
Henon-like attractor,
population dynamics,
simulation,
37D45 ; 92D25 ; 37M05,
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS],
[SDV.EE]Life Sciences [q-bio]/Ecology, environment
@article{hal-00679905,
author = {Arlot, Sylvain},
title = {Etude d'un mod\`ele de dynamique des populations},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {fr},
url = {http://dml.mathdoc.fr/item/hal-00679905}
}
Arlot, Sylvain. Etude d'un modèle de dynamique des populations. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00679905/