Dynamics Behavior Of A Predator-prey Competitive Model In Chemostat

In this paper,we mainly study the dynamics behavior of a predator-prey competitive model in the stirred Chemostat,that is the two types of microbes which may have both predator-prey and competitive relationships.The stability of equilibrium points,the existence of limit cycles,and the Hopf bifurcation are discussed when the consumption rate of nutrients is a linear function.There are three chapters in this paper.The first chapter is the introduction.We will introduce the history of development,research status of the Chemostat model and the preliminary knowledge.In the second chapter,we mainly study the dynamics behavior of a predator-prey competitive model in the Chemostat.Firstly,we obtained the existence and locally asymp-totic stability of equilibria in the model by qualitative analysis of differential equations.Secondly,by constructing an appropriate Lyapunov function,we discuss the global sta-bility of all equilibria points of the system.Finally,we consider some problems of Hopf bifurcation.In the third chapter,the mixed situation model with delays is studied.The global dynamics of the system is attained by analyzing the equilibria and their stability.