Dynamics of a Lotka–Volterra map
Volume 191 / 2006
Fundamenta Mathematicae 191 (2006), 265-279
MSC: Primary 58F13.
DOI: 10.4064/fm191-3-5
Abstract
Given the plane triangle with vertices $(0,0)$, $(0,4)$ and $(4,0)$ and the transformation $F:(x,y) \mapsto (x(4-x-y),xy)$ introduced by A. N. Sharkovski\uı, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior of the Schrödinger equation.
