Effect of fear on prey-predator dynamics: Exploring the role of prey refuge and additional food

The effect of induced fear in the prey due to the presence of a predator can alone develop anti-predator resistance to such an extent that it might reduce the prey reproduction in a significant amount. As fear can perceptibly affect the densities of the terrestrial vertebrates, here we investigate the cost of fear on a Holling type II predator-prey model associated with prey refuge and additional food to the predator. We evidently provide conditions on the existence and stability of equilibria as well as the occurrence of the Hopf bifurcation. Besides, we study how the presence of fear re-calibrates the effects of prey refuge and additional food in terms of quality and quantity on the system dynamics. We observe that the effect of fear not only reduces the predator density but also considerably drives the system toward stability. All the results presented here are mainly analytical but to make it more comprehensive, we perform numerical simulation. Moreover, to show the vast applicability of our results, we compare it with a few other models according to the presence of fear, refuge, and additional food.