Analysis Of Discrete Dynamical Model For Fishing Resources With Two Exclusive Economic Zones

This paper presents a discrete dynamical model of the marine fishery resourcesdivided two exclusive economic zones,on which the fish and fishing boats can beswimming. We simplify the model into a two-dimensional discrete system by the use ofaggregation methods and analysis the dynamics of system.On the one hand, we give the conditions of sustainable use for the resources byanalying the existences and local stabilities and bifurcations of the positive equilibria.Furthermore,we study the changes of attractors and the boundary of feasible domainsunder different parameters by the use of the method for dilimiting the boundary offeasible domains,which reveals the evolution of renewable resources.On the other hand, we establish a nonlinear fishery resources model with anexternal interfernce on the basis of the original model. By the help of MATAB andIDMC software to simulate the feasible domain of attractions, we discuss the sensitivityof the initial conditions which ensure that the resources is not extinct under the givenparameters by the use of the singularies theory and critical curve theory.