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

TL;DR

This paper investigates a complex infinite-dimensional population model, revealing the existence of attractors, including strange and novel types, demonstrating chaos can arise from density dependence and delay without seasonal effects.

Contribution

It introduces a new population dynamics model exhibiting complex attractors, including a previously unidentified attractor type, and analyzes the chaotic behavior arising from density dependence and delay.

Findings

Existence of attractors in the model's parameter space

Discovery of a new type of attractor in population dynamics

Chaotic behavior without seasonal variations

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.