A Modeling Dynamics for Fish Harvesting Resources with Taxation as a Control Variable

摘要

In this paper, we discuss a dynamic response model for a fishery. The dynamics of this system of halieutic resources in an aquatic environment includes two areas: a free area for fishing and a reserve. In our case, it is assumed that a reasonable catch rate function and an appropriate fee per unit of landed fish biomass imposed by an external organization. The existence, as well as the stability of possible equilibria, is carried out. Bionomic equilibrium of the system is determined and optimal harvest policy is studied with the help of Pontryagins maximum principle. Thus, a numerical simulation will be realized to approve our analytical results.