Control Problem, Based On The Optimization Of The Exploitation Of Biological Resources

Biospecies resource is a kind of regenerative resource. In order to make it possible forpeople to exploit and use biospecies resource duratively, we should give consideration tozoology benefit and economy benefit. The biological resources development research is car-rying on the qualitative analysis through the establishment mathematical model, Forecastingthe development of the population and the in?uence of people's development behavior tothe population.besides, establishing corrected capture strategy, which not only can main-tain ecosystem balance, but also can meet human needs. So its significance is particularlyimportant.In this paper, according to the study of biological populations model in domestic andforeign, especially, the development of biological populations with exploitation which is ap-plied broadly in reality, we mainly introduce following questions:First, The model of single population's increase is set. In this model, the harvestinge?ort is not a constant but variables changing with time. We prove the local stability ofequilibrium, when the equilibrium exist. Then making use of Maximum principle, we obtainthe optimal revenue and the optimal state. Finally, using the Bang-Bang control achievesshortest time to get the optimal state.Second, The exploited model of two species competitive system with periodic is con-sidered. Furthermore, We assume the regenerative resource is seasonal or regular. So adistinguishing feature of the model considered here is that the capture is the pulse occurs,which makes the model is more realistic. Firstly, It is shown that the periodic competi-tive system has a unique positive periodic solution which is globally asymptotically stable.Lastly, using of optimal impulsive control principle to discuss the optimal capture time andthe optimal population size.On the basis of the first, set up a predator-prey-type model with Bedding-DeAngelisfunctional response. Discuss the existence and globally asymptotically stability of equilib-rium. At last, obtain the most optimal capture strategy. At last, We set up a impulsive harvesting model of two species mutually beneficialsystem. Separately carries on the discussion for four di?erent kinds of exploitation forms.Furthermore, We assume that prices and costs are variables due to the change of harvestingpopulation sizes and harvesting e?orts. So a distinguishing feature of the model consideredhere is that using harvesting population sizes and harvesting e?orts to represent prices andcosts, which make the result more realistic. In order to safeguard the ecological balancebetter, we carry on the pulse capture when the population reach a certain number. Obtainthe optimal capture strategy.