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Global Stabilization of a Fish Population System Using Criteria Sample of Stability

In this article, we show global asymptotic stability of an equilibrium point of a non-trivial non-linear system of dimension 4 that modeled fishery model using a simple criterion of stability polynomial. By using the direct Lyapunov method, we develop a simple design technique, which allows to study the stability of the nonlinear system of fishing. And main objective is to obtain simple sufficient conditions used to obtain the stability of our system around the equilibrium point of reference. The proposed approach is that sufficient conditions demonstrate the overall stability of the system under study can be presented as feasibility tests. The results are tested by numerical examples.