Interspecies competition between prey and two different predators with Holling IV functional response in diffusive system

Abstract

This paper deals with a prey–middle predator–top predator ecosystem model with Holling type IV predator response in the unreserved zone. The model system is studied analytically and the threshold values for the existence and stability of various steady states are worked out. The global stability analysis is carried out. It is observed that if the intrinsic growth rate of prey population crosses a certain critical value, the system enters into Hopf bifurcation. The existence of bionomic equilibrium of the system has been discussed. Further, we study a path of optimal harvesting policy by introducing the Pontryagins maximum principle. Moreover we have found out a condition for diffusive instability of a locally stable equilibrium. Finally, some numerical simulations are performed to justify analytical findings.