A Class To Meet Mutually Beneficial Relationship Lotka-Volterra Biological Populations Optimal Control Problem

This paper is to study the problem of optimal capture of two biological popula-tions and mutually beneficial relationship Lotka-Volterra ecosystem.It’s conducted a comprehensive qualitative analysis to make the population trying to find feasible solutions to sustainable development.From the economic interests of economics per-spective, considering on the premise of population continued survival to maximize profit capture the optimal scheme.This paper is divided into three chapters,the specific content as followsChapter Ⅰ.introduces the research background biological mathematics.And de-scribes the research paper background.Chapter Ⅱ,gives some preliminary knowledge about the optimal control.ChapterⅢ,meet the biological populations studied Lotka-Volterra Cooperative System optimal control problem, a problem with the amount of control model and the stability of the equilibrium point,Thus its function to establish performance indicators based on income,and then use Pontryagin’s maximum principle to solve them,the most rewarding strategy.Finally, there is the use of simulation software to simulate them,indicating the reliability theory.Chapter V,studies the species of the Lotka-Volterra Cooperative System to es-tablish a more reasonable control parameters, namely the current one population increase in the form of differential equations with time trying to capture.we discuss local stability in each equilibrium point.We also discuss the optimal harvesting prob-lem of fishery resources in the reserve area. A regulatory agency controls exploitation by imposing a tax per unit biomass of the prey species.The objective is to maximize the monetary social benefit as well as conservation of the ecosystem.Finally,some numerical simulations are also given to illustrate our analytic results.In the final,we summarize the innovation of the paper and propose improving direction of the paper.