Analysis Of A Class Of Plankton Model

This thesis studies one kind of model about plankton, using the knowledge of the nonlinear analysis and partial differential equations, particularly, the fixed point index theory of elliptic equation and eigenvalue theory. We have studied the existence of positive steady solutions and the stability of semi-trivial solution.Firstly, this thesis studies the plankton model with constant growth rate N0We discuss the existence of positive steady solutions of this model by the method of upper and lower solutions and the degree theory. Then some intuitive results are given by the numerical analysis. Next the properties of Logistic model following is introduced, Finally, combining with the nature of the above study, we use the eigenvalue theory of elliptic equation to study the stability of semi-trivial solution about the model with inconstant growth rate and different diffusion coefficient with the different value of d1, d2.The main contents in this thesis are as follows:In chapter1, we introduce the background of this plankton model and the research works and results about the model.In chapter2, we study the model with constant growth rate. Firstly, we give the priori estimate about the model by the method of upper and lower solutions and the elliptical equation theory. We give the existence condition about positive steady solutions of this model by Leray-Schauder degree theory.In chapter3, we study the model with inconstant growth rate which related to space variable. Firstly, we give the existence condition and the stability condition of semi-trivial solution by nonlinear analysis. When the diffusion coefficient take different values. We give the stability of the semi-trivial solution by the eigenvalue theory of the elliptic equation.