Comparative studies on a predator–prey model subjected to fear and Allee effect with type I and type II foraging

Abstract

In ecology, the interactions between prey and predator can be direct or indirect. Predators can affect prey population by means of direct consumption and by inducing a non-consumptive fear effect in the prey population. In our present study, we investigate the impact of an indirect prey–predator interaction by considering the effect of fear of predation coupled with predation-driven Allee effect on the prey population. We propose and analyze two-species prey–predator models where the growth rate of prey is affected by a combined non-consumptive Allee-cum–fear effect induced by the predator and due to two different foraging behaviour of the predator. We investigate and compare the dynamical behaviour of the systems with Holling type-I and Holling type-II foraging rates of the predator. We observe that the system with type-II foraging rate of the predator has a wider basin of attraction of the stable coexistence equilibrium compared to the system with type-I foraging rate. We also observe that due to the gradual increase of fear level, the systems exhibit oscillatory dynamics followed by multiple stability switching.