A Dynamic Model Of The Persistent And Consistent Survivability Of A General Time-varying Gause-type Predator-prey Dynamic System And The Mechanism Of Algal Blooms

The Predator-prey model is a cooperative product between mathematics and ecol-ogy, and after more than one century's development there are flourishing achievements in correlative theory and its applications.The integration of mathematics and ecol-ogy meets the common need of mathematical science and ecological science, and it promotes mathematic advancement while providing solutions to ecological problems .Since 1960s,uniform persistence in ecological system has always been a heated issue .But in recent years most researchers have focused their work on specific models instead of general models. Some of the researchers have only given the necessary conditions for the uniform persistence of systems, and it constricts their application to a great degree. In respects of ecology, problems of environmental pollution attract most of our attention .Over 30 years of the Reform and Opening-up policy, China has made great achieve-ments and progress in economic development, but it has suffered irreversible damage to the environment.The issues of algal blooms and red tide have drawn great attention from relevant experts.However researchers from ecology often limit their work in qual-itative and statistic analysis rather than put their research on the evolution mechanism of phytoplankton and zooplankton in water body. Some of the experts have build math-ematical models to describe the dynamical behavior in the phytoplankton-zooplankton evolving systems, but it is a pity that they have neglected the fluctuation of climate and temperature brought by the seasonal variation which might affects the phytoplankton's growth rate, or that they have ignored the nutrient concentration in the polluted water body which might also have great influence on the phytoplankton's multiplication.This dissertation,motivated by investigating this serious ecological problem, makes research on the general time-dependent Gause-type Predator-prey model and has obtained a necessary and sufficient condition for the uniform persistence of the system and a sufficient condition for the existence of periodic solution of the system. On investigating the evolving mechanism of the phytoplankton and zooplankton,this dissertation,based on the experiment by former ecologists and taking into account the impact of temperature and nutrient concentration,has obtained a growth rate surface and carrying capacity surface of the Microcystis aeruginosa which consists of two in-dependent variables of temperature and TP concentration. In the use of radial basis functions interpolation method which based on the actual measured time-varying tem- perature data in water body, a temperature function of time is fitted, and then the binary functions of growth rate and carrying capacity are obtained, both of which take two variables:time and TP concentration.On the basis of these studies,the time-varying phytoplankton-zooplankton model is built.Simulation results of the model has proved to be a reasonable explanation of the phenomena of algal blooms and red tides.Simula-tion results with the changes of parameters provides a theoretical support to the bioma-nipulation method.The main content of this dissertation is listed as follows:Chapter 1 introduces the background of the main work in this dissertation, the basic knowledge of population dynamics and the current situation of environmental pollution , and in addition the main structure of this dissertation.Chapter 2 write a review of traditional Predator-Prey model and the earlier Phytoplankton-zooplankton model.Chapter 3 gives a detailed theoretical analysis on a general time-dependent Gause-type Predator-prey model.It has obtained a necessary and sufficient condition for the uniform persistence of the system,and in addition a sufficient condition for the existence of periodic solution of the system.Chapter 4 introduces the basic knowledge of eutrophication and its harmful conse-quences firstly. Secondly it introduce the Basic method of radial basis functions inter-polation method. Then it presents the process of obtaining the growth rate surface and carrying capacity surface by using of radial basis functions method,and subsequently the time-dependent phytoplankton-zooplankton model with nutrient concentration pa-rameter. It provides a rational explanation to algal blooms and red tides by simulation results and the sensitivity of the system with respect to the change of the parameters, it also reasons the bio-manipulation technology in preventing eutrophication of water body.Chapter 5 concludes the work of this dissertation and give some topics for the future work.