Microbial Continuous Culture Model Of Qualitative Analysis

In this paper, two models with single and competitive species are studied. The main results of the paper are following: Based on bifurcation theory, the Hopf bifurcation of a special two-dimention Chemostat system is studied; The existence of periodic solution of three-dimention Chemostat system is discussed where the consumption rate for microbe growth to nutrition is linear function .The paper consists of three chapters:In chaper 1, the meaning of studing the Chemostat model is explained; Some definitions and preliminary theorems are introduced.In chaper 2, a specific two-dimension Chemostat system is discussed when growthrate μ(S/x) satisfies Monod-type. The existence of limit cycle by Hopf bifurcation theory is obtained. Meanwhile, using form series method we discuss the stability of periodic solution.In chapter 3, three-dimention competitive model is studied. First, we obtain the results about stability of equilibrium under microbe growth rate μ(s) in direct proportion function. Second, using Zhang Zhifen's uniqueness theory, we obtain the existence and uniqueness of periodic solution when microbe growth rate satisfies Monod-type. We also discuss Hopf bifurcation ,and obtain stability of periodic solution with succeed function method.