Bifurcations of a Leslie Gower predator prey model with Holling type III functional response and Michaelis-Menten prey harvesting

TL;DR

This paper analyzes the stability and bifurcations of a predator-prey model with Michaelis-Menten prey harvesting, revealing complex dynamics including Hopf, saddle node, and Bogdanov-Takens bifurcations through rigorous proofs and simulations.

Contribution

It provides a comprehensive bifurcation analysis of a Leslie-Gower predator-prey model with nonlinear prey harvesting, including the first proof of Bogdanov-Takens bifurcation in this context.

Findings

Existence of Hopf bifurcation

Presence of saddle node bifurcation

Identification of Bogdanov-Takens bifurcation

Abstract

We discuss the stability and bifurcation analysis for a predator-prey system with non-linear Michaelis-Menten prey harvesting. The existence and stability of possible equilibria are investigated. We provide rigorous mathematical proofs for the existence of Hopf and saddle node bifurcations. We prove that the system exhibits Bogdanov-Takens bifurcation of codimension two, calculating the normal form. We provide several numerical simulations to illustrate our theoretical findings.