Renewable Resources Optimization And Qualitative Analysis

In the real word, some of the sources are nonrenewable, and the others are renewable, and the biological resource is one of the renewable resources. How to scientifically exploit,utilize and manage the biological resources has been become an important subject for study in mathematics, ecology and management etc. The quantity of harvest is an important index for the exploitation of the biological resource, but its price and the most interest must also been considered two important factors; In addition, in the optimal exploitation,utilization and management of the biological resource, in order to realize the sustainable exploitation, it is not only reasonable but also necessary to consider the dynamical influence of the harvesting behavior and the human economic to the biological resources, and hence to depict the dynamical relationship between human exploiting behavior and the population development.In this dissertation a kind of the optimal models with the objective function to maximize the total discounted net economic revenue and the stability of the two-species predator-prey system with the age-structure and the functional response are studied. The dissertation consists of four chapters.The first chapter is the introduction, the significance and the foreground are presented, the outline and the main results are given;The second chapter is to study a kind of the optimal models with the objective function to maximize the total discounted net economic revenue. By using the maximum principal, especially, the method of the Hamiltonian function, in the dynamical optimization,the expressions of the optimal control function and the optimal state orbit are given, such that the objective function is optimal during a given interval, that is, economic revenue is maximal;The third chapter is to study the two-species predator-prey system with the age-structure and the functional response, and the conditions which the steady states are locally stable,especially, the stability is studied when one of the characteristic roots of the singular point is zero, which was not studied in some references, in the meantime, some wrong results in one of the references are put forward;The last chapter is the part that summarizes the paper and propose some aspects which we may continue to work.