Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting

Year 2023, Volume: 6 Issue: 1, 1 - 18, 31.03.2023

Debasis Mukherjee

https://doi.org/10.33434/cams.1171482

Cited By: 1

Abstract

This article studies a discrete-time Leslie-Gower two predator-one prey system with Michaelis-Menten type prey harvesting. Positivity and boundedness of the model solution are investigated. Existence and stability of fixed points are examined. Using an iteration scheme and the comparison principle of difference equations, we find out the sufficient condition for global stability of the positive fixed point. It is shown that the sufficient criterion for Neimark-Sacker bifurcation can be developed. It is observed that the system behaves in a chaotic manner when a specific set of system parameters is chosen, which are regulated by a hybrid control method. Examples are provided to illustrate our conclusions.

Keywords

Predator-prey model, Leslie-Gower, Michaelis-Menten type prey harvesting, stability, bifurcation, chaos control

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