Periodic Solution Of Several Classes Chemostat Microorganism Cultures Models

In this paper, we study several classes chemostat microorganism cul-tures modelsseveral types, The article is divided into three chapters.The preface is in chapter 1, we introduce some knowledge of biology mathematics and the main work.In Chapter 2, We study the effect of the impulsive and delay in microorganism. In the first section, we introduce and study a model of a uptake function with Holling III and a predator-prey with Monod type functional response under periodic pulsed conditons, which contains with predator, prey, and periodically pulsed substrate. We investigate the subsystem with substrate and prey and study the stability of the peri-odic solutions, The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurca-tion theory, we prove that above this threshold there are periodic oscil-lations in substrate, prey and predator. Furthermore, by comparing bi-furcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period-doubling and period-halving. In the Second section, we introduce and study a mode of a Beddington-DeAngelies chemostat model with delayed growth response and pulsd input concentration of the nutrient in a pol-luted environment. The sufficient conditions for the golbal attractivity of microorganism-extinction periodic solution were obtained.In Chapter 3, we introduce and study a chenmostat model involving distributed delays with two-nutrients and nutrients recycling. Some suffi-cient conditions ensuring the existence and global attractivity of periodic solutions for the chemostat model are derived by employing the theory of coincidence degree and differential inequality technique.