Periodic And Almost Periodic Solutions Of Some Time-delay Differential Equations

Many practical problems in the fields of biology,physics,economics and so on can be described by delay differential equations,and many mathematicians devote themselves to the study of the qualitative properties of such systems.In this paper,a biological dynamics model based on delay differential equation is mainly studied.By using the comparison theorem of differential equation,the cone fixed point theory of Banach space,the extension theorem of the solution of functional differential equation and the theory of almost periodic ordinary differential equation,the dynamic properties of the time-delay predator-prey model with Beddington-De Angelis type and the variable delay hematopoiesis model with generalize nonlinear are discussed.The uniform persistence,global attractiveness and the existence and uniqueness of positive almost periodic solutions of the system are presented.The full text structure is as follows:The first chapter introduces the background and current situation of the study,and briefly summarizes the main work of the paper.In the second chapter,the sufficient conditions for the uniform persistence for a class of time-delay Beddington-De Angelis type predator-prey systems are studied by using the comparison theorem.In the third chapter,by using the cone fixed point theory of Banach space,the sufficient conditions for the existence of positive almost periodic solutions of a class of generalized nonlinear hematopoiesis model with variable time delay are further improved and generalized.In the last chapter,on the basis of the third chapter,the sufficient conditions for the uniform persistence of a class of generalized hematopoiesis model are obtained by using the extension theorem of the solution of the functional differential equation,and the sufficient conditions of the global attractiveness of the system are given by using the theory of almost periodic ordinary differential equation.