Evolution of the population of Microtus Epiroticus: the Yoccoz-Birkeland model

• Main Authors: Nieto, Juan José, Pacifico, Maria José, Vieitez, José Ladislau
• Format: Report
• Language: unknown
• Published: arXiv 2011
• Subjects: Dynamical Systems math.DS; FOS Mathematics; 37M05, 37N25, 92D25; Birkeland; Lambda; Svalbard; Microtus epiroticus
• Online Access: https://dx.doi.org/10.48550/arxiv.1101.5543; https://arxiv.org/abs/1101.5543

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. : 33 pages, 5 figures