Abstract:

We study when the celebrated May-Leonard model in $mathbb{R}^3:$

[x'= x(1-x-ay-bz),y'= y(1-bx-y-az),z'= z(1-ax-by-z),]
describing the competition between three species and depending on two positive parameters $a$ and $b,$ is completely integrable; i.e. when $a+b=2$ or $a=b.$ For these values of the parameters we shall describe its global dynamics in the compactification of the closed positive octant, i.e. adding its infinity.