Chaos Control And Synchronization In 2-D Discrete Dynamical Systems

2-D discrete dynamic systems is an important part of delay large systems, belonging to the field of multi-variable discrete time sequence in control theory. Dut to its i-mportance in solving practical problem and its wide-ranged applications, it has become an academic research area in recent years. In this thesis, basic research on qualitative theory and control of 2-D delay discrete dynamic systems is performed. The content is divided into different categories shown as follow:Section I The stability analysis of the linear and nonlinear 2-D delay discrete dynamic systemsExperimental results are given in boundary stability and exponential stability for the linear system. For the nonlinear system, an important transformation is introduced in the process of mathematical analysis. Then, the stability problem of 2-D delay discrete dynamic systems can be solved effectively. Also, it offers the basis of theory for the control of 2-D delay discrete dynamic systems.SectionII Structure of spatially periodic orbit and chaotic behaviour in the sense of Li-YorkFor the iteration problem of spatially multi-variable sequence, it is not only a heart problem of spatial orbit of motion in research progress, but also an important concept. In this thesis, an iterative method of spatial sequence is given. Then, spatially k -periodic orbit is produced and its basic criterion of spatially chaotic behaviour is obtained in the sense of Li-York.Section III The stability of spatially periodic orbit and chaotic behaviour in the sense of MarottoBased on the production of periodic orbit in the 2-D discrete dynamic systems, its qualitative analysis of boundary stability is given. Also, the spatially chaotic behavior in the sense of Marotto in 2-D nonlinear discrete dynamic systems is dis- cussed, and on spatial Lyopunov are also obtained.