Study The Mathematical Behavior Of Several Types Of Biochemical Differential Equation System

In this paper, the stability-properties of three types of differential system are studied. In the Chapter 1 , by using the stability theory of ordinary differential equation the singular points of a biochemical systemare discussed. Firstly, singular points of the linear approximation system of the biochemical system are specifically classified. Secondly , it is proved that besides p=0 the singular points of the biochemical system and it's linear approximation system are in the same type. In the Chapter 2, by means of bifurcation theory, the sufficient condition for the existence of positive solutions of cooperative model with saturationis obtained: a > 1, b > 1,, and for the proof for the sufficientconditions for the existence of positive solutions, it is listed three lemmas in the paper, of which the proof for two lemmas is given. In the Chapter 3, a sufficient condition for the existence of a global asymptotically point in a classic n-dimensional Lotka-Volterra systemis proved by Liapunov function method (or V function method) in the stability theory. The condition is changed into another equivalent form. The new criteria can be validated more easily, and bas been applied to a special Lotka-Volterra System. At last, it is extended to more fields, for example new-product selling system and epidemic disease spreading system etc,Main Results of Chapter 2 was published on the Journal of Shaanxi Normal University ( Sum No. 19, 2003).Graduate's Name : Ablimit ABDIRYIM(Differential Equations) Directed by DOU Ji-hong...