Qualitative Stability Patterns for Lotka-Volterra Systems on Rectangles

摘要

We present an analysis of the Lotka-Volterra differential equation within rectangles that are transverse with respect to the flow. In a similar way to existing works on affine systems (and positively invariant rectangles), we consider nonlinear LV equations, in rectangles with any kind of tranverse patterns. Notably, we give conditions for the existence of such rectangles. We also analyze the dynamical behavior inside a rectangle. This work is a first step towards a qualitative abstraction and simulation of Lotka-Volterra systems.