Analysis & Studies On The Predator-Prey System's Dynamics With Population's Diffusion And The Influence On Biodiversity

The study on population dynamic model is the important part of population ecology, and the objects of this study are population quantity trends, space trends, structure trends and so on. Under every condition the number of the population changes with the variety of time under the factor of external functions. The effect of all kinds of factors, esp. when the living environment of the population is polluted, can often cause changes of population substance–sometimes depopulation, while sometimes continual surviving. Consequently, using the mathematics model to investigate the population quantity in polluted environment is the effective way of the pest's prevention and cure or the protection of wild animals.In the process of the pest's synthetic prevention and cure, the job includes not only the pest's prevention and cure but also the protection of the pest's natural enemy population that feeds on them. Otherwise, the pest's natural enemy population will become extinct for having no nothing to eat, and this kind of job will cause the loss of biodiversity, which runs counter to the pest's synthetic prevention and cure. Therefore, the pest's synthetic prevention and cure is to control the pest population within certain amount scope, so that they will not explode on a large scale to endanger plants and economic benefits. Meanwhile, the pest's natural enemy population will gain the continual living for having food, and the two populations will form relationship between the preying and the prayed to control changes of pest's amount. When the pest's living environment is polluted, if another living space can be built, then when the pest spreads in the two living sections, only to control the diffusion rate artificially and reasonably is able to guarantee the pest's amount within the permitting scope. It also guarantees the continual living of the pest's enemy population. It will control the amount of the pest population through the controlling of their enemy population.The study builds the following model on the above aspects:Firstly, when the toxin infects the prier's living section and cannot diffuse, the quantity dynamic model between the preyed population and the preying population in another living section is as following.Through discussing the model the thesis concludes the term for Yu value of the preyed population's continual living and depopulation and the conclusion of the preying population's inevitable depopulation.Secondly, when the toxin infects the living section of the preyed and the preyed population can diffuse into another section, population dynamic model on the predator–prey system in the two sections is built . The thesis discusses the term for the two populations'continual living and exterminates in this system, and achieves a conclusion the system condition is related to diffusion rate of the preyed population in the two sections.Thirdly,when the toxin infects the living section of the preyed and the preyed population can diffuse into another section,the time delay dynamic model on the predator–prey system with diffusion of the preyed population in the two sections is built .And the thesis discusses the terms for the populations'continual living.which relate to diffusion rate of the preyed population in the two sections.Finally.through discussing the effect of diffusion on ecosystem, the thesis further analyzes that the population diffusion will change the biodiversity in the system.