Research On Chaos Anti-control And Synchronization In Dynamical Systems

Since Lorenz found the first chaotic attractor in a three-dimensional autonomous system in 1963, the study of chaos has become an important research topic. Due to the extreme sensitivity of chaotic systems to initial conditions, for a long time, chaos was considered to be a harmful form of movement. So over the past decades, a lot of researchers have devoted to finding new methods for suppressing and controlling chaos. As technology advances, chaos is found to have a good application prospect in many areas, such as signal generator design, secure communication, fluid mixing, etc. Recently, chaos anti-control by means of making an originally non-chaotic dynamical system chaotic, or enhancing existing chaos, has attracted increasing attention.This article is in connection with nonlinear chaos anti-control study, the main contributions are listed as follows:Firstly,a new chaotic system is proposed. Some basic dynamical properties are studied. Utilizing the feedback control method, the linear and nonlinear feedback controllers are designed for the novel system. Based on Lyapunov stability theory, the sufficient condition for stabilizing chaos to unstable equilibria is obtained. The theoretical analysis and simulation results are given to show the effectiveness of the method.Secondly, the synchronization problem of this proposed chaotic system is studied. While system parameters are known, synchronization of this system is realized by using generalized synchronization method. Then, combining the Lyapunov stability theory with adaptive control technique, the adaptive controller and the parameters update law are constructed for this chaotic system with uncertain parameters. In addition, the sufficient condition of the synchronization is derived and strictly theoretical proof is also given. Numerical simulations demonstrate that the synchronization of this chaotic system can b e achieved and the unknown parameters can be identified simultaneously.Finally, the problem of chaos anti-control for nonlinear chain system is studied. According to the nature of chaos anti-control of a chaotic system, single input and multiple input nonlinear feedback controllers are designed by introducing tracking control subtly. Then chaotification of chain system is successfully realized by tracking reference chaos system.