Modeling And Control For A Class Of Fishery Population

The fishery resource is a kind of important renewable resources. For the fishery resources sustainable development and utilization of human, ecological benefits and economic benefits need to be considered at the same time. The research of the fishery resources, qualitative analysis are through the establishment of mathematical model, and then, we predict the development of the species, and the effects of people’s development behavior effects on populations. Thus, determining the correct capture strategy and making the fishing population resources can maintain the balance of ecological system and meet the need of human development, thus the study of fishery population resource has very important practical significance.The presented paper discusses the modeling problems for prey-predator systems and the optimal taxation policy problems on the basis of nonlinear dynamic system theory, optimal control theory and other related control theory. The work of this paper contains the following aspects:A prey-predator system with tax policy is established and the existence and the locally asymptotic stability of the equilibrium point are analyzed. The harvesting efforting is time-varying. The exploitation of biological resources are governed by taxation. It poves the existence of the equilibrium point, and locally asymptotic stability of them. Finally, by choosing appropriate Lyapunov function, it proves that positive equilibrium point is globally asymptotically stable.The optimal control problem for a prey-predator system with taxation policy is studied. Based on the theory of the net revenue cost, the optimal capture strategy problem is investigate. In order to determine the tax control to make net revenue cost maximum, by using Pontryagin maximum principle, the optimal tax policy is obtained.Finally, the main work of the thesis is summarized, and the potential research topics for further work are pointed out.