The Stage-Structured Single Population Model With Harvesting

The single population model with stage-structure has very complicate dynamical properties. Especially under linear state feedback and some constant harvest, this model displays various complicated dynamic features , including the changes of the positive equilibrium and stability and the emergence of bifurcation, as well as the result of the change of the maxim harvesting in economics. After learning of these dynamic properties, we can properly exploit the population, on the precondition of the persistence, make it offer resources for human for ever.This thesis may be summarized as follows:Firstly, we study the effcct of linear state feedback on the dynamical characteristic for the model, received the different numbers of equilibrium under the different conditions, such as static bifurcation, and also get the efficient and necessary conditions for the model to have stable positive. And we discuss the affection to the model of the constant harvest, obtain the efficient and necessary condition for the model to have stable positive equilibrium, bifurcation. And also get the maxim income of such system.Secondly, we study the affection of the harvesting to the system , giving the maxim profit what we can get when we exploit only one stage and when we exploit both the two stages of the community ,on the precondition of the persistence of the community.Thirdly, we study the characters of the model when the harvest efforts depends on the profit, get the different condition under different suppose to make the model stable.At last, we consider use the tax action of the government to adjust the market, to make sure that the natural resources live forever. And also we discuss how to gain the maximal economic profit by maximum principle under ecological balance.