Preprint D85/2011
Evolution of the population of {\it Microtus Epiroticus}: the Yoccoz-Birkeland model.

José Ladislau Vieitez | Nieto, Juan José | Pacifco, Maria José

**Keywords: **
Evolution of populations | Dynamics of Populations | Populational Evolutions | Homoclinic Point | Chaos

We study the discretized version of a dynamical system given by a model proposed by Yoccoz and Birkeland
to describe the evolution of the population of
{\it Microtus Epiroticus} on Svalbard Islands,
see ${\rm http://zipcodezoo.com/Animals/M/Microtus\_\,epiroticus}$.
We prove that this discretized version has an attractor $\Lambda$ with a hyperbolic 2-periodic point $p$ in it.
For certain values of the parameters the system restricted to the attractor exhibits sensibility to initial
conditions. Under certain assumptions that seems to be sustained by numerical simulations, the system is
topologically mixing (see definition \ref{topmix}) explaining some
of the high oscillations observed in Nature. Moreover, we estimate its order-2 Kolmogorov entropy obtaining
a positive value. Finally we give numerical evidence that there is a homoclinic point associated with $p$.