Holling Type Response Function in Fishery Modelling with Optimal Harvesting Policy

In this paper, we have considered a very general Holling type predator-prey system with selective harvesting and where both of the species follow logistic growth. The uniform boundedness of the system has been studied together with the conditions of existence. Also, we have obtained the criteria for local stability of various equilibrium points then considering suitable Lyapunov function, the global stability of the system has been discussed. After that using Pontryagin Maximal Principle, we have studied the optimal harvesting policy for the system. At the end, the problem has been illustrated through some numerical examples. Finally, we have discussed the problem with the help of a numerical example by using arbitrary feasible parametric values and using MATLAB, we observed from stability diagram (Fig. 1) and phase portrait (Fig. 2) that as the values of decreases, the steady state value of Prey population increases. This is quite good result for ecological sustainability of species. Our model may be extended by incorporating time delay and stochasticity in the system.