Dynamics of a discrete-time Beddington–DeAngelis predator–prey model with fear effect

In this paper, we explore the impact of fear on a rather simple predator–prey system with Beddington–DeAngelis functional response in a discrete-time setup. We consider reduction in the birth rate of the prey population due to the cost of fear of the predators. We analytically derive the existence and local asymptotic stability criteria of all the fixed points of the system. In addition, we also determine the conditions for the occurrence of flip and Neimark–Sacker bifurcations. By performing numerical simulations, we show that increasing the strength of fear, irregular oscillations can be removed and the system’s dynamics can be stabilized. We also find that an increment in the parameter, related to the mutual interference of the predators, can stabilize the system. However, further increase in the parameter value leads the system toward chaos.