Analysis of A Tritrophic Food Chain Model with Fear Effect Incorporating Prey Refuge

Abstract

In this work, we have introduced a tritrophic food-chain model where consumer hunt for prey with Holling type-III functional response. The birth rate of the prey population has been reduced due to the fear of predation, i.e., a fear effect is considered in the prey population. Moreover, a fraction of the prey is available to the consumer for consumption and this has been done by incorporation of prey refuge term. The predation between consumer and predator follows Beddington-DeAngelis response. The occurrence of transcritical bifurcations have been shown and conditions for the existence of a limit cycle in the system through Hopf bifurcation also have been stated. Both the analytical and numerical results suggest that a certain amount of fear can make the system steady. It is also noted that the prey refuge has both stabilizing and destabilizing effect on the system.