DYNAMICS OF A PREDATOR–PREY MODEL WITH CROWLEY–MARTIN FUNCTIONAL RESPONSE, REFUGE ON PREDATOR AND HARVESTING OF SUPER-PREDATOR

Abstract

In this paper, a three-species food chain model has been developed by considering the interaction between prey, predator and super-predator species. It is assumed that in the absence of predator and super-predator species, the prey species grow logistically. It is also assumed that predator and super-predator consume prey and predator, respectively. It is assumed that the predator shows refuge behavior to the super-predator. Again, harvesting of super-predator population has been considered. It is assumed that the consumption of prey and predator follows Crowley–Martin-type functional form. Boundedness of the solution of the system has been studied and different equilibrium points are determined and the stability of the system around these equilibrium points has been investigated. Existence conditions of Hopf bifurcation with respect to [Formula: see text] of the system have been studied. It is found that the system shows some complex and critical dynamics due to increase of handling time of prey. It is also found that the system moves towards stable steady state due to increase of predator interference. It is observed that predator refuge may be responsible for the stability of the system. The chaotic dynamics of the system have been found due to the increase of the harvesting rate of super-predator.