Local and Global Stability Analysis of a Predator-Prey System with Harvesting and Fear Effects

To analyze predator-prey dynamics, this study introduces a novel mathematical model that combines two key human-induced elements, harvesting and fear effects, and the predator’s access to other food resources. Our model thoroughly describes the complex interactions of ecological systems by combining birth and death rates, predation rates, prey growth rates, and the potency of the fear effect. We identify a range of dynamical behaviors within the system through meticulous mathematical analysis, which includes determining the equilibrium point and stability evaluations. The sustainability of prey populations and the stability of entire ecosystems are further illuminated by our research, which also examines the resilience and vulnerability of ecosystems. We conduct numerical analysis to examine the local and global stabilities of the equilibrium points. The stability results show that the equilibrium points are locally stable under a parametric condition involving the birth rate, harvesting rate, and fear level. Furthermore, the predator-free and interior equilibrium points are globally asymptotically stable under a parametric condition. Our theoretical research and numerical simulation demonstrated that fear and harvesting effects significantly influence the dynamic behavior of this model.