Global phase portraits of a predator–prey system

Abstract

We classify the global dynamics of a family of Kolmogorov systems depending on three parameters which has ecological meaning as it modelizes a predator–prey system. We obtain all their topologically distinct global phase portraits in the positive quadrant of the Poincaré disc, so we provide all the possible distinct dynamics of these systems.

Keywords

• predator–prey system
• kolmogorov system
• global phase portrait
• poincaré disc