On the Dynamic Regulation of a Non Linear Model Fish Population

Abstract

In this work we deal with the stability property of a discrete-time nonlinear model of a harvested fish population with the Beverthon-Holt recruitment relationship. We use the method of Lyapunov functions to show that the positive equilibrium state of the stage structured model fish corresponding to a constant fishing intensity is globally and asymptotically stable. Since the fishing intensity is often variable, we also propose how a variable fishing intensity may be controlled through feedback in order to stabilize the fish population state around the positive equilibrium state.