| In this paper, the common fishery resource is simplified, containing only one kindof fish, the single-species fishery resource is subdivided into two zones, a protected areaand a fishing area, the fish migrates only between the two areas, and the protected areahas no fishing behavior.First, the discrete dynamical model of single-species fishery with a protected areais established, based on research of some scholar, such as B. Dubey, G.I. Bischi, T.K.Kar, and so on.Second, through the theoretical derivation, conditions of existence and uniquenessof the positive equilibrium are given, and the mathematical proof is given; the localstability and bifurcation of nonnegative equilibrium is studied, and numerical simulationis used to verify the local stability and bifurcations of nonnegative equilibrium, thiswork is done by some mathematical software, such as MATLAB, IDMC, and so on.At last, the global method is used to analyze the structure of feasible domain. Onthe one hand, give a constant value to the proportion of protected area, we begin toanalyze the change of the attractors and the boundary of feasible domains by changingof the fishing efforts; on the other hand, give a constant value to the fishing efforts, webegin to study the change of the attractors and the boundary of feasible domains bychanging of the proportion of protected area. Then, we have obtained the conclusionthat the fishing efforts and the proportion of the protected area have significant impacton the sustainable regeneration capacity of the fishery resource.After the above discussion, we expect to obtain the conditions on the sustainableutilization of the single-species fishery resource. |
