Abstract

We describe the dynamics of the 3-dimensional competitive Lotka–Volterra systems x˙=x(a−x−y−z),y˙=y(b−x−y−z),z˙=z(c−x−y−z), providing the phase portraits for all the values of the parameters a, b and c with 0 < a< b< c in the positive octant of the Poincaré ball.