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 $p$.

Anexos:

• ratfinal.pdf