Final evolutions of a class of May-Leonard Lotka-Volterra systems

Abstract

We study a particular class of Lotka-Volterra 3-dimensional systems called May-Leonard systems, which depend on two real parameters a and b, when a + b = -1. For these values of the parameters we shall describe its global dynamics in the compactification of the non-negative octant of Double-struck capital R-3 including its infinity. This can be done because this differential system possesses a Darboux invariant.