A fishing strategy for the stabilization of a continuous harvested fish population stage structured model

Abstract

The aim of the paper is to design a fishing strategy in order to regulate an exploited fish population. To this end, we consider a stage structured continuous model of a harvested fish population. This model includes   1 n stages represented by their abundance ( ) i X t , stage 0 being the pre-recruits stage. Each stage is characterized by its fecundity, mortality and predation rates. We gave a formula for the fishing effort as an output feedback control that allows to stabilize the system. We first gave a sufficient condition for the system to be globally stable around the reference equilibrium. Then the global stability behavior of the positive equilibrium is studied via the output feedback control. The same problem for the continuous stock recruitment model has been addressed in our previous work [9]. Simulations results of the continuous fishery systems confirm the effectiveness of the proposed design.