Poincar\'e map construction for some classical two predators - one prey systems

TL;DR

This paper develops a method to construct Poincaré maps for a classical predator-prey system with two predators and one prey, enabling analysis of system dynamics especially when both predators survive.

Contribution

It introduces a way to build positively invariant sets for these systems, facilitating the study of their long-term behavior through Poincaré maps.

Findings

Construction of positively invariant sets for the system

Definition of Poincaré maps in the context of predator-prey models

Application to classical examples from prior research

Abstract

In this paper we consider a family of system with 2 predators feeding on one prey. We show how to construct a positively invariant set in which it is possible to define a Poincar\'e map for examining the behaviour of the system, mainly in the case when both predators survive. We relate it to examples from earlier works.