Dynamical Behaviors Of One Kind Of Non-autonomous Chemostat Model

In this paper, the non-autonomous growth Chemostat models with generalresponse functions are considered. In models, the dilution rate and removalrate are allowed to be the same. And the uptake rate do not only dependon the nutrient but also the time. Making use of basic theory of ODE andinequality technics, we obtain criteria of global asymptotical stability of non-autonomous single-population Chemostat model, and basing on the results ofsingle-population model, a su?cient condition is obtained to assure the perma-nence of non-autonomous two population Chemostat model. Considering therelationship between the permanence and extinction, we give a su?cient condi-tion to assure the extinction of the population.The organization of this paper as follow.In the first chapter, we introduce the background of the development and thepresent main work about Chemostat model, which are from autonomous systemto non-autonomous system, from without time delay to with time delay.In the second chapter, a Chemostat model with general uptake function areconsidered, by means of reducing the dimension, criteria are derived for there toexist a globally asymptotical stable positive solution.In the third chapter, the permanence of chemostat model with two popu-lations are considered. To end it, we make use of the relation between singlepopulation system and two population system. In addition, the extinction ofchemostat model with two populations are considered. Comparing the result ofpermanence, the criteria which we obtain is not perfect, so we give a conjectureabout extinction of biomass.