ECOLOGICAL SUSTAINABILITY OF AN OPTIMAL CONTROLLED SYSTEM INCORPORATING PARTIAL CLOSURE FOR THE POPULATIONS

Abstract

This paper describes a prey–predator fishery model incorporating partial closure for the populations. It is assumed that the predator population partially dependent on a logistically growing resource with Beddington–De Angelis type functional response. The proposed system also reflects the dynamic interaction between the net economic revenue and the fishing effort used to harvest the populations. The steady states of the system are determined and the dynamic behavior of the system is discussed. The existence of Hopf bifurcation phenomenon is examined at the interior equilibrium point of the proposed system. We have adopted partial closure for the populations as a controlling instrument to regulate the harvesting of the populations. A dynamic framework towards the optimal utilization of the resource is developed using Pontryagin's maximum principle. The optimal system is numerically solved using an iterative method with Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve a sustainable ecosystem. Results are analyzed with the help of graphical illustrations.