Several New Continue Chaotic Systems: Basic Dynamics Character, Control And Synchronization

With the chaos control and anti-control increasing, and the emergence of new chaotic attractors and chaos control methods, chaos anti-control study in the discrete system has been better researched. But the research in a continuous system is far from reach maturity. How to generate the new continuous chaotic attractor using feedback control method, and present more effective control strategy for the continuous chaotic system, which is one of the issues of common concern. Purpose of this subject apply anti-control of thoughts and methods to construct several new continue chaotic system, which provide more continuous chaotic model for the practical application of chaos theory. In addition, studies of chaotic control and synchronization of some control strategies, combined with a large number of chaotic systems, numerical simulations are given to show the effectiveness of this method. The new chaotic attractors will help us enhance the understanding of chaos. Meanwhile, the new control and synchronization method will enrich the existing chaos control and synchronization methods. The paper made the following aspects of the research.First, after introducing the motive and the significance of chaos control and synchronization, then, we gave out the main contents and the innovations of this study.Second, chaos control and synchronization were summarized in this paper. We introduced the definition and characteristics of chaos, chaos control and synchronization features, and focused on research situation of the control and synchronization.Next, we gain five new chaotic systems by using the method of chaotification, and some basic dynamical properties are studied. The five new chaotic systems possess the following features. The first new chaotic system is gained by feedback controlling Lorenz chaotic system, according to the definition of generalized Lorenz system, and the system still belong to generalized Lorenz systems. The second new chaotic system is gained by feedback controlling Lorenz systems, according to the definition of generalized Lorenz system, and the system does not belong to generalized Lorenz systems. The third new chaotic system has five terms, in comparison with those of the existing six-term or seven-term chaotic attractors, the new attractor is simpler and fewer terms. The fourth new chaotic system is a single parameter chaotic system, which can generate a complex 4-scroll chaotic attractor, a 3-scroll chaotic attractor, and two 2- scroll chaotic attractors with variation of single parameter. The fifth new chaotic system is four-scroll chaotic attractor in three-dimensional autonomous system, in comparison with those of the existing four-scroll chaotic attractors, the novel chaotic attractor can generate four scrolls two of which are transient chaotic and the other two of which are chaotic.Then, we discuss control of the new chaotic system. Firstly, we present hybrid dislocated control method for stabilizing chaos to unstable equilibrium and limit cycle. Secondly, the control method of dimension reduced is presented. And the trajectories of a chaotic system can be controlled to approach arbitrary points or arbitrary target periodic orbits by the control method of dimension reduced.Furthermore, we discuss synchronization of the new chaotic system. First, we present hybrid general hybrid projective dislocated synchronization, which includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. The drive and response systems discussed in this paper can be strictly different dynamical systems (including different dimensional systems). Second, we investigate the different bidirectionally coupled chaotic systems, which includes identical bidirectionally coupled synchronization. Third, we investigate the problem of adaptive lag synchronization and parameters adaptive lag identification of chaotic systems. In comparison with those of the existing parameters identification schemes, the unknown parameters are identified by adaptive lag laws and the delay-time is also identified. Fourth, we investigate hybrid synchronization, in comparison with those of the existing synchronization methods, the hybrid synchronization includes full-order, reduced-order synchronization and the modified projective synchronization. What's more, the control, complete synchronization and anti-synchronization can coexist in the same system. Fifth, we investigate the problem of adaptive synchronization of chaotic systems with adaptive scaling function. In comparison with those of the existing scaling function synchronization, the scaling function is also identified. Sixth, we discuss a note on synchronization quality of chaotic system. Finally, we investigate the synchronization of a general complex dynamical network with non-derivative and derivative coupling. Based on LaSalle's invariance principle, adaptive synchronization criteria are obtained.