Modified Projective Synchronization And Function Projective Synchronization Of Several Chaotic Systems

As a complex nonlinear dynamics behavior, chaos is a general phenomenon in nature. At the beginning of 1990's, chaos synchronization was presented. Since then, chaos synchronization has become a hot spot of research due to its potential applications such as in secure communication, information science and biotic science.In this thesis, we mainly consider the modified projective synchronization and function projective synchronization of chaotic systems. By using the adaptive control law and the impulsive control scheme and combining with the Lyapunov stability theory, we discuss the modified projective synchronization and function projective synchronization of some classic chaotic (or hyper-chaotic) systems. Meanwhile, the synchronization of some fractional systems is also discussed. This thesis is categorized into five parts and the organization is as follows.In the first chapter, the definition of chaos, synchronization and the synchronizing methods are given, also, the main contents of this paper are briefed.The second chapter addresses the function projective synchronization problem of two unified chaotic system in the presence of unknown system parameters. Based on Lyapunov stability theory two adaptive control laws are proposed to make the states of two identical chaotic systems asymptotically synchronized according to the number of parameters. By this method, one can achieve chaotic synchronization and identify the unknown parameters simultaneously. Numerical simulations are presented to show the effectiveness of the proposed schemes.Modified projective synchronization of the fractional Lorenz system is theoretically and numerically studied by three different methods in the third chapter. The sufficient conditions for achieving synchronization of the fractional differential systems are derived by using the stability criterion of fractional linear equation. Numerical simulations show the effectiveness of the proposed methods.The forth chapter investigates the impulsive control and modified projective synchronization of the Lorenz hyper-chaotic system. We give some sufficient conditions for the stabilization and modified projective synchronization of this system via impulsive control. Simulation results are also provided to show the effectiveness of the proposed method. It is easy to see by Theorem 4-4 that if the scaling factorsα1,α2,α3,α4 satisfiedα12=1,α2=α1α3=α4, then systems (4.4) and (4.11) will achieve modified projective synchronization without controllers.In the fifth chapter, the research work of this thesis is summarized and the possible direction is further proposed.