Fishing activity in the Atlantic Moroccan Ocean: Mathematical modeling and optimal control

Abstract

As it spans the Mediterranean sea and the Atlantic Ocean on the north and west respectively, Morocco is characterized by its marine sources’ diversity. Fishing Activity is considered to be the backbone of the country’s economy. the process of structuring the exploited population, and the marine environment are two major fields that the kingdom must understand to implement management measures to sustain the equilibrium of national fisheries and marine sources. Here, we have built a discrete-time model to describe the dynamic of fishing of two small pelagic species on the Atlantic Coast. The equilibrium between marine population and fishing effort, and maximizing profit are what the control parameter proposed have to achieve. We use a discrete version of Pontryagin’s principal maximum to calculate the optimal system. The numerical simulation is carried out using Matlab.