A global mathematical investigation of a predator-prey model

TL;DR

This paper develops a comprehensive global bifurcation diagram for a predator-prey model described by a specific plane differential system, enhancing understanding of the system's long-term dynamics.

Contribution

It provides the first complete global bifurcation analysis of this predator-prey model, revealing the system's complex behavior and stability properties.

Findings

Identification of all bifurcation points.

Classification of equilibrium stability regions.

Description of possible long-term dynamics.

Abstract

We construct a global bifurcation diagram of the plane differential system $$ {l} \dot x = x(1-x)-x y/(a+x^2), \dot y = y(\delta-\beta y/x), x(t)>0, y(t)>0, a>0, \delta>0, \beta>0, $$ which describes the predator-prey interaction.