On the Dynamic Regulation of a Non Linear Model Fish Population

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Résumé

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.

Mots-clés

fish population dynamics, nonlinear population models, discrete-time models, stage-structured population model, Lyapunov function, global asymptotic stability, positive equilibrium, feedback control, population regulation