Study On Synchronization And Control Method For A Class Of Chaotic Systems

The chaos synchronization and control have the broad application prospects in many research fields. Since the chaos synchronization and control have been proposed, they have the potentially important role in both communications of the information science and the bio-medical engineering of life sciences. These make the chaos theory become a hot spot of research. Currently people have made some progress on the chaos synchronization and control method of research, but the study of chaos synchronization and control is not yet understand and grasped fully, the chaos synchronization and control are still the science foreland. It is a significant and far-reaching issue that we will study the chaos synchroniza-tion and control in depth and use the chaos theory in human social services effectively. It has caused a great of concern from a large number of researchers. In this paper, we have studied the chaos synchronization and control in depth. Some works are including the proposing of a new class of complex and chaotic systems and their attractors and the development of im-proved various synchronization and control methods in several chaotic systems. The works have enriched the content of the chaos theory and have certain theoretical and application value. The main research and innovation in this paper are as follows.1. A new double-scroll chaotic transition system and its unified system are proposed. A new classification of critical conditions is given. Another simple transition systems-Lu-like system has been found. The Lu-like system is also the transition system between the Loren system and Chen system. A simple new double scroll chaotic unified system with one parameter is also introduced, which unifies the above three different chaotic systems. And finally, a detailed study has been done on the dynamics and features of these two new chaotic systems.2. A new type of three-scroll chaotic system and its unified system are presented and studied. The new three-scroll chaotic systems are three-dimensional smooth family of non-linear autonomous systems with squared items, but they all have the three scroll chaotic attractors with the different topologies. Among them, some basic behavior features of this type chaotic dynamical system have been made some in-depth analysis and research, such as Lyapunov index, fractal dimension, cycle window, the local bifurcation, Poincare cross section and fractals. Constructing a three-scroll chaotic unified system with a variable to control and achieving the smooth transition among the three-scroll chaotic systems.3. Proposing a new type of four-dimensional fractional super-chaotic system and studing its basic dynamic behavior. Combined with Chen fractional super-chaotic systems and Lu fractional super-chaotic system, the different fractional super-chaotic system synchroniza-tion has been studied in depth. Based on the fractional calculus theory and Laplace transform theory, using fractional order systems stability theory and computer simulation techniques fully, presenting the design method of the nonlinear state controller and designing a nonlinear state controller. So a different class of nonlinear fractional order super-chaotic systems with different structure can be achieved synchronization. This synchronization method is strict. The design is simple, and easy to implement. The synchronization error can convergence fast and the time for achieving synchronization is short.4. Study on the chaotic synchronization and anti-synchronization for the uncertain new super-chaotic system and three-scroll chaotic unified system based on the active pinning control technology. At the same time, proposing the active control technology strategy which only controls a state of uncertain chaotic systems. That is one controller needed to realize the synchronization and anti-synchronization between the drive system and the response system, and ensure the robust stability of the synchronization for the uncertain chaotic system and three-scroll chaotic unified system. The theoretical analysis and numerical simulations show that the chaotic synchronization and anti-synchronization can be achieved within a relatively short time by this controller in the uncertain new super-chaotic system and three-scroll chaotic unified system, respectively.5. Study on the generalized projective synchronization with the adjusted scale factor about a class of antisymmetric chaotic systems with different structures. A new control design method is proposed, and a stable controller is designed to control the synchronization of chaotic systems with the tridiagonal structure. Giving the sufficient conditions for stability of the chaos system, and then proving that it is the stable source asymptotically for state error of the system. So that the general projective synchronization with the adjusted scale factor can be achieved between the antisymmetric chaotic systems with different structures. Subsequently, we focused on the stability control of chaotic synchronization for the systems with the tridiagonal structure, and also proposed a new control design method. Based on the design method recursively for the system with the tridiagonal structure, the original nonlinear affine system is transformed into the stable system with a special tridiagonal structure. The chaotic synchronization is achieved after the controller acting on the transformation chaos system. The coupling coefficient between the drive system and response system has a new broad interpretation. The method will be used in many practical nonlinear control problems, which can reduce the cost. Numerical simulations show the validity and reliability of the method.6. An adaptive control method and parameters update law are designed to guarantee stabilize the new super-chaotic system with unknown parameters. Proposing the new adap-tive synchronization controller and parameters updating rules, and stabilizing the system to an unstable equilibrium point. Based Lyapunov stability theory and adaptive control the-ory, the chaos synchronization is achieved among the two same super-chaotic systems with unknown parameters or two different ones with unknown parameters. Subsequently, the projective synchronization has been achieved and studied in depth on a new type of super-chaotic system with variable scale factor. Furthermore, numerical simulations verified the flexibility and effectiveness of the new proposed synchronization method.