Qualitative Analysis On Two Types Of Ecosystem Models

According to the two kinds of microorganisms compete for the same kind of nu-triation,the thesis discusses the differential equation group model of two ecological s-ystems and establish a differential equation model.Then,Considering pollutant sourceof poison in the survival environment is influential in breeding microorganisms.thethesis introduce the inhibitor function into equation group and establish the second d-ifferential equation models. This thesis consists of four chapters.The first chapter is the introduction.This part introduces the background of bio-mathematics,describe the simple device and working principle of laboratory chemos-tat and at the same time,contains the domestic and foreign mathematics researchersdiscussion of research actuality and research significance on the chemostat.The second chapter gives some mathematical definitions and related theorem.The third chapter discuss two kinds of microorganisms compete for the same n-utriation model:Analyze nonnegative invariance of system, construct the Lyapunov function tostudy the global asymptotic stability properties and the extinction of boundary equili-brium.further application of the three-dimensional Hopf bifurcation theorem and Hu-rwitz criterion discuss the presence of Hopf brifurcation in boundary equilibrium andthe range for the existence of periodic solutions.The fourth chapter introduce the inhibitor function to the chemostat competitivemodel, then establish the model as follows: We obtain the sufficient conditions for the boundedness of the solution to the s-ystem and the global asymptotic stability properties and the extinction of equilibriumin view of the Lyapunov function. Furthermore, further programming, the thesis usesMatlab software to simulate asymptotic behavior of the above equations in the inter-nal equilibrium.