Effect of Fear in Leslie-Gower Predator-Prey Model with Beddington-DeAngelis Functional Response Incorporating Prey Refuge

In the present paper, we study the effect of antipredator behavior due to fear of predation on a modified Leslie-Gower predator-prey model incorporating prey refuge which predation rate of predators follows Beddington-DeAngelis functional response. The biological justification of the model is demonstrated through non-negativity, boundedness, and permanence. Next, we perform the analysis of equilibrium and local stability. We obtain four equilibrium points where two points are locally asymptotically stable and other points are unstable. Besides, we show the effect of the fear in the model and obtain a conclusion that the increased rate of fear can decrease the density of both populations, and prey populations become extinct. Meanwhile, for the case with a constant rate of fear, the prey refuge helpful to the existence of both populations. However, for the case with the fear effect is large, prey refuge cannot cause the extinction of predators. Several numerical simulations are performed to support our analytical results