The Study Of Optimal Control Problem Of Exploitation And Management On Biospecies Resource

Biospecies resource is a kind of regenerative resource which can keep balance through adjustment by itself . People exploits to use it through four phases :"deficient exploitation,accelerative increase , excessive exploitation and resource management". During exploitation and management, zoology benefit and economy benefit usually are the principle of exploitation ,which make it possible for people to exploit and use biospecies resource duratively. In the last twenty years, the problem of biospecies resource on exploitation and management is always an active field for research. Many scholars do a great deal of research works on different problems with different sides .This paper stresses on two aspects. The first is exploitation and management on single biospecies resource. According to the theory of chemical adsorption and biospecies nutriology, we sets up a increscent model of a single biospecies, then, discusses the problem of the optimal control on the price of biospecies resource changes with the reap quantity, and studies the game theory problem: the optimal reap quantity of Cournot monopoly and the problem of imposure management, adjustment of exploitation on biospecies resource. Then we come to three conclusions that under the condition of long-term exploitation on biospecies resource, the optimal reap quantity is confirmed by the two boundary of the systemic saddle dot, the optimal trajectory tend gradually towards the systemic optimal balance dot through the feedback to reap quantity; and find that the optimal reap quantity of the two main exploitation body is distributed according to theshadow income of the biospecies resource and the optimal revenue policy is dirving system to the optimal bioeconomics equilibrium dot as soon as possible. The second is the study of the exploitation and management on multibiospecies resource. Above all, with the theory of the optimal control, we study the optimal policy of simultaneous reap and detached reap on the two biospecies of competitive system, and get the profit level affected by the discount rate of the reap boispecies, The cost price of detached reap is higher than simultaneous reap. Then we discuss an actual problem, analyze a homeostasis relation of natural enemy-mouse, establish a optimal control model on the number of arresting and killing and the optimal prevention and cure model on using pesticide to kill mouse. Through the answer to the model, we affirm the optimal quantity of the natural enemy and the optimal quantity of the pesticide, which offers the theory for prevention and cure on mouse.