Dynamical Analysis For The Fishery Resources Information

As an important branch of ecology，population ecology explain，forecast and controlpopulation through analysis population model. As one of the most important subjects whichapply mathematics in the ecology widely, population ecology is effectively pushed aheadby the ideas and research methods of mathematical modeling. With the help ofmathematical theory and methods, people can clearly reveal the rule of populationevolution and predict the tendence of its development. When putting it to practice, themodels are tested and corrected, so that the modified model can reflect the reality better.Fishery has become one of the pillar of the economy in China. The pessimistic fact isthat fishery industry underwent several times decelerate since the1980s. There are manyreasons cause this phenomena, such as overfishing, marine pollutants, marine project andso on. Though fishery resources are renewable, overfishing will result in resourcesexhausting and ecological disasters. So, fishing rate should not surplus the self-renewallevel, then a relatively stable output can be achieved.There are two basic research aspects in population study: on the one hand, to lookingfor the evolution rules of the population; on the other hand, to strengthen artificialintervention on population, such as protection, exploration, etc. More and more scholarsapply mathematical ideas and research methods to the investigation of fishery. A lot ofresearch results of fishery modeling are achieved, for example, fishery production model,fishery efficiency model.Taking marine fishery resources as the research background, using differentialdynamical system method, we analysis the rule of population evolution and the influence ofthe human activity on population in this paper. In Chapter2, we study the optimalharvesting strategy of the species with Smith type growth rate. To ensure the feasibility ofharvestng, we study the exisitence of positive equilibrium first. Based on the stabilityresults, by the simple mathematical analysis, we obtain the optimal harvesting strategy andthe optimal species density. In Chapter3, we study the optimal harvesting strategy ofinshore-offshore species. We obtain the stability of the system by Liapunov method. Basedon the stability analysis, the optimal harvesting strategy is obtained. In Chapter4, we studythe stability of time-delay Smith model. Two type time delays added into Smith-type model,the influence of delay on stability are investigated. In Chapter5, based on the stabilityanalysis of differential system, we obtain the stability criteria for infect-free equilibrium ofa class of endemic disease by the Lyapunov method. This stability criterion is thereproduction ration is less than1.