<p>The current work investigates a mathematical model for predator and prey population dynamics, considering nonlinear prey harvesting and hunting cooperation between predators. The positivity and boundedness of the solutions have been discussed, and the stability of the system’s equilibria has been examined. The results show that over-harvesting can lead to the extinction of the prey population, while hunting cooperation can increase the predator population. In addition, the possibilities of Hopf-bifurcation and saddle-node bifurcation in the system were investigated. A study of bifurcations, such as saddle-node and Hopf-bifurcations concerning critical parameter thresholds, increases the understanding of the system’s dynamics. The novelty of this study lies in integrating harvesting and hunting cooperation into the predator-prey model. This allows for a better understanding of how these ecological factors influence system dynamics, including the evolution of complex behaviors and various stable equilibria. Furthermore, the proposed mathematical model, analytical findings, and simulations contribute significantly to sustainable resource management strategies.</p>