Bioeconomic model of zooplankton–phytoplankton in the central area of Morocco

Abstract

Marine planktonic ecosystems are highly dynamic environments that are subject to a wide range of external forces. This paper presents the conditions for local and global stability of a bioeconomic problem concerning the harvesting of phytoplankton and zooplankton in Moroccan areas. The problem of determining the fishing effort that maximizes the net economic revenue of each fishing boat results in a generalized nash equilibrium problem. Growth of both organisms is governed by parameters as well as externally applied nutrients and the biomass of the other species available as supplemental nutrition. More precisely, we are interested in the equilibrium of the mathematical game given by the situation where all the fishing boats try to optimize their strategies according to the strategies of all the others. The importance of marine reserve is analyzed through the obtained results of the mathematical analysis of the proposed system.