A SUFFICIENT CONDITION OF A POLYNOMIAL FISH POPULATION SYSTEM TO BE STABLE

Abstract

In this paper, we use Lyapunov approach to study the stability of an exploited fish population system. The model considered is structured in n age classes and includes a nonlinear polynomial stock-recruitment relationship. Lyapunov candidate functions is investigated and sufficient conditions for global asymptotic stability of the studied polynomial system are proposed to allow computational implementation. The results obtained extend our previous study focusing on the solution to the same problem solved using other tools of control engineering. The advantage of the proposed approach is that the derived conditions proving the stability of the studied systems can be presented as in inequality in general and feasibility tests. The obtained results are tested by numerical examples.