Dynamical behavior of prey-predator system with reserve area and quadratic harvesting of prey

The present paper deals with mathematical modeling of a fishery resource system in an aquatic atmosphere consisting of two zones: a free fishing zone and a reserved zone, where fishing is strictly prohibited. The dynamics of the system is studied in the presence of bird predator. In this paper, the quadratic harvesting of the fish species in unreserved zone has been considered whereas bird predator species is subjected to linear harvesting. All the possible biological and bionomic equilibria of the system are studied extensively for their existence, local as well as global stability. We have found various ranges of harvesting parameter for maintaining the Sustainability in the proposed ecosystem. Optimal harvesting is discussed using Pontryagin's maximum principle. Numerical simulations are done to support the theoretical results obtained.