Global phase portraits of a predator-prey system

TL;DR

This paper classifies all possible global phase portraits of a predator-prey ecological model, providing a comprehensive understanding of its dynamics depending on three key parameters.

Contribution

It offers a complete classification of the global dynamics of a family of predator-prey systems in the positive quadrant, based on three parameters.

Findings

All topologically distinct global phase portraits identified

Complete characterization of system dynamics in the ecological context

Provides a foundation for understanding predator-prey interactions

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 Poincar\'e disc, so we provide all the possible distinct dynamics of these systems.