Asymptotic Behavior And Convergence Of Several Classes Of Delayed Biodynamic Models

With the development of science and technology,the application of delay differential equations in physics,engineering,biology and economics has been ex-panding.They are often used to explain many natural laws and phenomena in the real world.Especially,it has played an important role in the study of the problems of ecology system,neural network and the spread of epidemics and so on,so it has a wide application background to continue the theoretical and applied research of delay differential equation.In this doctoral dissertation,the asymptot-ic behaviors and convergence of several non-autonomous time-delay biodynamic systems,including population growth and epidemic transmission models,Lasota-Wazewska Model of Respiratory Dynamics and Hematopoietic Dynamics,cellular neural networks,are studied by using the basic theory of delay differential equa-tion,differential inequality techniques based on mathematical analysis,fluctuation lemma,contraction mapping principle and Lyapunov method.New results have been obtained.The effectiveness of the results has been verified by numerical simulations of several specific examples.The dissertation consists of the following seven chapters:In Chapter I,we summarize the historical background and the trend of de-velopment of the research topic,and briefly describe the main work of this paper.In Chapter 2,the asymptotic behavior of solutions of two-dimensional non-autonomous differentia.l equa.tions is studied by using differentia.l inequa.lity tech-nique and Dini derivative theory.The famous Bernfeld-Haddock conjecture is extended to the case of two-dimensional non-autonomous differential equations.It is found that under given initial conditions,each solution of the system is bounded and tends to be a constant vector.In Chapter 3,we discuss the asymptotic behavior of solutions of non-autonomous scalar neutral functional differential equation with time-varying delays.The main result obtained by using differential inequality technique and Dini derivative the-ory show that the solution of the system is bounded and tends to a constant at last.This result generalizes the Haddock conjecture.In Chapter 4,the global convergence of the positive equilibrium point in the Lasota-Wazewska model with multiple time-varying delays describing the survival of red blood cells in an animal is discussed.By using the differential inequality technique and fluctuation lemma,a condition is obtained for the influence of the delay on the global attractiveness of the model.The results show that the positive equilibrium point of the system is a global attractor under the small delays.In Chapter 5,we present a new result on the existence,uniqueness and gener-alized exponential stability of almost periodic solution of cellular neural networks with neutral-type proportional delays and D operator.Some sufficient condition-s for the existence and global generalized exponential stability of almost periodic solution of cellular neural networks are obtained by using the contraction mapping principle and differential inequality techniques.In Chapter 6,some sufficient conditions for the global exponential convergence of a class of high-order cellular neural networks with neutral type proportional de-lays and D operators are established by using differential inequality techniques,contraction mapping principle and Lyapunov functional method.The main re-sults of this paper show each solution of the system exists and global exponential converges.The results provide a new light for the design of stable high-order cellular neural networks with neutral-type proportional delayIn Chapter 7,we established sufficient criteria to guarantee the existence and globa.l exponential stability of positive equilibrium point of SICNNs with multiple proportional delays via differential inequality analysis and Lyapunov method,and illustrates that the system considered is eventually positive.