The Optimal Harvesting Problem Of Biological Resources

Biospecies resource is a kind of regenerative resource. In order to make it possible for people to exploit and use biospecies resource duratively, we should give consideration to zoology benefit and economy benefit. The biological resources development research is carrying on the qualitative analysis through the establishment mathematical model,forecasting the development of the population and the influence of people's development behavior to the population. Besides, establishing corrected capture strategy, which not only can maintain ecosystem balance, but also can meet human needs. So its significance is particularly important.In this paper, according to the study of biological populations model in domestic and for- eign, especially, the development of biological populations with exploitation which is applied broadly in reality, we mainly introduce following questions:Firstly, the exploited model of two species system is considered .In this model, the harvesting effort is not a constant but variables changing with time. People control exploitation by imposing a tax per unit biomass of the prey species. We prove the local stability of equilibrium, when the equilibrium exist. The problem of optimal taxation policy is then solved by using Pontryagin's maximum principle.Secondly, the paper deals with a prey-predator model incorporating a prey-refuge and harvesting. Both the species are harvested where we use the usual catch-per-unit-effort hypothesis. The dynamical behavior of the exploited system is examined. Then consider the existence of a bionomic equilibrium. The optimal harvesting policy is studied by using Pontryagin's maximal principle.Thirdly, by taking into consideration the environmental factors to restrict the growth of the population, we discuss the effects of toxicants released by some other species in a food chain system in which only the prey specie are harvested. The local and global stabilities are examined. The possibility of existence of a bionomic equilibrium is considered. The optimal harvesting policy is studied by using Pontryagin's maximal principle.Lastly, this paper investigates the dynamical behavior of an exploited system consisting of two predators and a prey which is being harvested. The existence of biological, economic and optimum equilibrium of the system is examined. Then analyze the local stability of the model. The optimal harvesting policy for harvesting the prey species is studied.