Global dynamics of 3D type- K monotone Lotka–Volterra system with the identical intrinsic growth rate

Source abstract

Abstract In this paper, we classify all global dynamics of the three-dimensional type- K monotone Lotka–Volterra system with the identical intrinsic growth rate inside the compactification of the positive octant of R 3 $\mathbb {R}^{3}$ double struck upper R cubed . By means of the replicator equations, it is proved that this system can have exactly 35 $35$ 35 topologically different phase portraits. As a consequence, we obtain the necessary and sufficient condition for the system to be bounded in the positive octant and verify that the limit set of any orbit of the compactified vector field associated with the system is an equilibrium.