Two Kinds Of Discrete Dynamic Systems With Time-delay Stability And Bifurcation Analysis

In this paper, we discuss and analyse the stability and bifurcation of two discrete dynamic systems with delay. There are three chapters.In Chapter1, the development of the nonlinear dynamic system, rational difference equation and a list of bifurcation theory are described, respectively.In Chapter2, we discuss the stability and direction of the bifurcation of a discrete Mackey-Glass model with delay. Firstly, I study the linear stability of the model by characteristic equation and verify the existence of Neimark-Sacker bifurcation and flip bifurcation. Then we get the direction and stability of the Neimark-Sacker bifurcation and flip bifurcation by using the bifurcation theory of discrete dynamical systems. Finally, the analytical results are right by numerical simulations.In Chapter3, we study the stability and direction of the bifurcation of a third-order rational difference equation with positive parameters. Firstly, we discuss the linear stability of the equation. Secondly, we get the direction and stability of the Neimark-Sacker bifurcation. Finally, the analytical results are right by numerical simulations.