Bifurcation Analysis of a Leslie-Gower Prey-Predator Model with Fear and Cooperative Hunting

Abstract

The current work examines the dynamical features of a Leslie-Gower prey-predator model. The effects of fear and group defense among prey with the mechanism of cooperative hunting by predators are incorporated. The existence and uniqueness of the interior equilibrium are explained. We obtained sufficient conditions for the local and global stability behavior. With regard to the fear parameter and cooperation strength parameter, the proposed system undergoes Hopf-bifurcation, transcritical bifurcation, and saddle-node bifurcation. Moreover, the system exhibits the property of bi-stability between two interior equilibrium points. The basin of attraction of these points is also plotted. All theoretical results are verified numerically by MATLAB R2021a.