Hopf Bifurcation And Optimal Harvest For A Predator-prey Biological Economic System With Price Changed

Throgh this paper，a series of harvesting models with price changed with demandand supply as theme were studyed. We thought about the stability and optimal harvestof a biological economic system with single population and one with prey-dependentpredator-prey. The Hopf bifurcation of a predator-prey model with price changed withdemand and supply was next discussed. The full text was divided into five chapters.The first chapter was the introduction.At first we introduced the background ofraising of the research problem.Then we introduced the research status of this field.The second chapter is about prerequisite knowledge. It discussed the stability andoptimal harvest of a biological economic system with single population. The localstability of equilibrium point was studied by the stability theory of differentialequations，the maximum sustainable yield wasd iscussed through dynamics analysis，and last，the government tax revenue was given.Chapter Ⅲ is one of the main elements，an economic harvesting model ofprey-dependent is established. After a bio-economic explanation of the model，weanalyze the local stability of positive equilibrium point in detail，and naturally get thecriteria for local stability. Maximum sustainable yield is given through dynamicsanalysis when the permanence of prey is guaranteed. Similarly，the revenue with pricechanged with demand and supply is studied and the maximum revenue is presented.The differential-algebraic system of chapter Ⅳ is expanded from the differentialsystem of Chapter Ⅲ. Here we discussed the stability and Hopf bifurcation of a kindof biological economic system which considers a prey-dependent prey-predatorsystem with price changed with demand.We selected the delay for branch parameters，and discussed the stability on the positive equilibrium point and existence of the Hopfbifurcation using of ordinary differential equation qualitative and stability theory andmethod.