  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.
