Bifurcaciones de Hopf: Análisis Cualitativo y Aplicación a un Modelo Bioeconómico de Pesquerías

This paper deals with the theory of codimension one bifurcations applied to a dynamical system derivedfrom applying Pontryagin 's maximum principIe to an optimal control problem for economic fisheries management. Changes in the number and/or the stability of stationary states as well as the appearance of closed orbits, are analyzed. Some necessCl.'Y and/or sufficient conditions are established for the existence of Hopf bifurcations, according to the biological and economic param'eters of the modelo We focus our attention on the resulting limit cycles which can be candidates for solutions of the optimal control problem. The method is applied to the South Atlantic "chamelea gallina" fishery. To obtain the bifurcation values, we have made numerical computations by the use of Content and Vensim software. So,we make a qualitative description of the trajectories behaviour around the stationary states.