Branch Research In Two Kinds Of Discrete And Continuous System

In the fields of nonlinear science,power system is one of the main components.Through the research on system dynamics behavior because of the foundation and development of Poincar?0)?Lyapunov and Birkhoff,the stability and branch problem have develop into important research topic in study fields of power system.Stability reflects the structural balance.The branch is some characteristics of the system occur mutations when the parameters change and pass a certain threshold values.This paper shows the rich dynamics behavior of two kinds of discrete and continuous dynamic system by using the normal theory?the center for popular theorem and the branch theory.On the research of the dynamic characteristics structure of discrete time dynamic system,we focus on the studying of the branch and the chaos phenomenon of a discrete infectious diseases model using the forward Eule? method.This paper derived the existence conditions and determine formula of stability of periodic solutions of two kinds of important bifurcations,and with the aid of numerical simulation,we clearly observe there appear stable period window,period-doubling overlap,leaping change of the dynamic behavior of periods to chaos and chaos to stable period windows.On the study of continuous system,we explore the change law of the chaotic dynamic system with a delay feedback control along with changes of branch parameter and the effect of the feedback controller to control the chaos.First of all,using center manifold type,specification and Hopf theorem,we gain the existence conditions of Hopf branch and branch expression of judging direction and stability of periodic solutions of a branch.Second,With the help of numerical simulation we get chaos can be controlled,delayed feedback control can induce stable cycle closed track.