GLOBAL DYNAMICS OF A PREY–PREDATOR MODEL WITH HOLLING TYPE III FUNCTIONAL RESPONSE IN THE PRESENCE OF HARVESTING

In this paper, we have investigated global dynamics of a two-species food chain model with the Holling type III functional response that includes linear harvesting for the prey and nonlinear harvesting for the predator. The long-time continued existence of both species is discussed using uniform persistence theory. Stability of various equilibrium points is described in terms of model parameters. The local asymptotic stability of non-hyperbolic equilibrium points is determined with the help of center manifold theorem. Global behavior of solutions of the model system when both species are present is determined by considering the global properties of the coexistence equilibrium. Here, we have taken a comprehensive view by considering different bifurcations of co-dimension one and two and have discussed the importance of various model parameters on the system dynamics. The model system shows much more complex and realistic behavior compared to a model system without any harvesting, with constant harvesting or linear-yield harvesting of either or both of the species. Numerical simulations have been conducted to illustrate the theoretical findings.