- Communications in Advanced Mathematical Sciences
- Vol: 6 Issue: 1
- Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michae...
Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting
Authors : Debasis Mukherjee
Pages : 1-18
Doi:10.33434/cams.1171482
View : 11 | Download : 6
Publication Date : 2023-03-31
Article Type : Research
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