<p>In the present study, we consider a discrete one prey-two predators system. Of the two predators, one is strong while the other is weak and unable to access a fraction of the prey population i.e., prey refuge. We have studied the permanence of the model and explored various fixed points with their stability dynamics. The threshold values for some parameters indicating the feasibility and stability conditions of some equilibria are determined. Analytically, we have investigated the existence of the periodic points as well as Hopf and Flip bifurcations. We have also investigated the range of significant parameters under which the system admits different bifurcations. Extensive numerical simulations were performed to validate the analytical findings. The existence of chaos and its possible control are also discussed in this context. These results can be applied to real-world ecological systems improving conservation strategies and the management of predator–prey dynamics. </p>