The Study Of Dynamics On Two Classes Of Turbidostat Models With Distributed Delay

With the rapid development of biomathematics in recent years,the research of biomathematics has been widely applied into many domains such as population dynamics,epidemics dynamics,microorganism cultivation and etc.The corresponding results could allow us to explain many practical issues during the growth and development of the population such as the growth of the microorganism in the turbidostat(chemostat).With the help of functional differential equations and ordinary differential equations,this thesis analyzes the dynamical behaviors of two kinds of turbidostat models,and specific numerical instances are presented to certify the conclusions.The thesis has three chapters,and the summarization is as followed:The first chapter introduces the research backgrounds and status of the functional differential equations and microorganism cultivation,and also lists the main contributions that have done in this thesis.In chapter two,a single-species turbidostat system with Monod functional response and distributed delay is constructed.By the theory of functional differential equations,central manifold theorem and normal form theory,the sufficient conditions of the existence and directions and stability of the periodic solutions are derived in this chapter.This chapter also investigates the destabilization of the periodic solutions about the wash out rate.Corresponding numerical simulations are given to certify the theoretical conclusions at the end of this chapter.In chapter three,a competitive turbidostat system with non-monotonic functional response and distributed delay is analyzed.The conditions of the existence for the equilibria are obtained using the basic properties of continuous functions.This chapter further establishes the sufficient conditions of the global stability of the equilibria with the help of the appropriate Liapunov-like functionals related to the theory of functional differential equations and ordinary differential equations.In the end,several specific instances are presented to certify the availability of the main results in this chapter.