Analyzing the Effect of Fear, and Refuge on Prey, Harvesting, and Hunting Cooperation Among Predators on Leslie–Gower Predator Prey Model

This paper analyzes a modified Leslie–Gower predator–prey model incorporating fear and refuge effects on the prey, along with hunting cooperation among predators and linear harvesting of the predator population. The model’s dynamical properties including boundedness, positivity, extinction criteria, and the existence and stability (both local and global) of equilibrium points are rigorously examined. Bifurcation analysis is also conducted to explore Hopf, transcritical, and saddle-node bifurcations. The study demonstrates that fear has a stabilizing effect on the system dynamics, while prey refuge, hunting cooperation, and harvesting can induce instability. Analytical findings are supported by extensive numerical simulations, which illustrate how variations in these ecological factors influence population dynamics and bifurcation thresholds. The findings provide insight into the intricate interactions between ecological and behavioral elements in predator–prey relationships.