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The Study on Several Types of Biochemical Reaction Models and Chemostat Microorganism Culture Models

Author: KongLiLi
Tutor: JiaJianWen
School: Shanxi Normal University
Course: Applied Mathematics
Keywords: Biochemical reactions Model Limit cycles Chemostat Time delay Impulsive input Permanence
CLC: O175
Type: Master's thesis
Year: 2010
Downloads: 28
Quote: 0
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Abstract


In this paper, we study several types of biochemical reactiont models and the delayed growth reponse and impulsive input in microorganism culture models. The article is divided into three chapters.In chapter 1, we introduce some knowledge of biology mathematics and the main work.In Chapter 2, by using qualitative theory of ordinary differential equa-tions,we study two biochemical reaction models. section one, we study the conditions of the existence, nonexistence and uniqueness of limit cycles of a reversible saturated biochemical reaction system are completely obtained and gave its qualitative depth map. section two, we study a model with irreversible saturated reaction. The necessary and sufficient conditions for the system has the limit cycles surrounding the positive equilibrium are obtained. And it is proved that if there exist the limit cycles, then the uniqueness of the limit cycles follows.In Chapter 3, we study the effect of impulsive input and time delay growth reponse in microorganism culture. Section one, we study a B-D-type chemostat model with time delay. By using the comparison theorem of differential equation and Lyapunov-LaSalle invariance, an analysis on existence and boundedness of solutions for the model and local asymptotic stability of its equilibria are carried out, it is shown that, while the interior equilibrium is not feasible, the washout equilibrium(i.e.boundary equilib-rium) is globally asymptotically stable for any time delay. Section two, we study a Monod-Haldane Chemostat Competitive Model with delayed growth reponse and impulsive input. By using corresponding theories and methods of impulsive delayed diferential equation, the sufficient conditions for the global attractivity of microorganism-extinction periodic solution are obtained, it is proved that the system is permanent under appropriate conditions. The results show that time delay is profitless and the impact of competition on the microorganism culture is small.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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