  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
Microtus Epiroticus on Svalbard Islands, see
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 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.
