Qualitative Analysis On Chemostat Competition Model With Two Different Functional Response

In this paper, two competition models of the chemostat is considered.Firstly,for the bad breath of human,we must use drug treatment to eliminate it.So after the assumption of ration-dependent increasing rate function,we set up the ordinary differential equations models for the relations between human oral microorganism populations.In the model, we add an external inhibitor and a new uptake function.we study the qualitative analysis of chemostat model.The global stability of the interior equilibrium are discussed by using Liapunov function.Then, We consider the chemostat model with different mortality rates, production constants and n populations competing for the same nutrients.we obtained the survival conditions of species,and dissipation of the standard system,and conduct qualitative analysis. This thesis consists of four chapters.In the first chapter,we firstly introduce the development,background and the meaning of the biomathematics.Secondly,we simply describe the working principle and the related results.Finally,the research status of chemostat model was introduced.In the second chapter,gives some mathematical definitions and related theorem.In the third chapter,we establish the model of chemostat with two microorganism populations.we study the stability of the boundary equilibria and interior equilibrium.Because the boundary equilibria are unstable,the interior equilibrium is stable,we discussed the global stability by using Liapunov function.In the model,we replace the Monod function with the functionSkx m SSf+)(=.In the forth chapter,introduces the chemostat model with different mortality rates, production constants and n populations competing for the same nutrients.we obtained the survival conditions of species,and dissipation of the standard system,and conduct qualitative analysis...