The Modified Projective Synchronization And Generalized Function Projective Synchronization Of Hyperchaotic (Chaotic) Systems

This thesis mainly studies the modified projective synchronization and the generalized function projective synchronization of hyperchaotic systems. By using the adaptive control law and the stability theory of linear system and combining with the Lyapunov stability theory, we discuss the modified projective synchronization,function projective synchronization and the generalized function projective synchronization of some classic chaotic (or hyperchaotic) systems. 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.A hyperchaotic system is defined as a chaotic system with at least two positive Lyapunov exponents, implying that its has more complex dynamical behaviors and could possibly be used in many fields such as chaos-based encryption, secure communication, biological systems and neural networks, etc. However, most of the publications usually assume that precise models are available. but in practical situation, some system's parameters are unknown or/and uncertain, and the synchr-onization will be destroyed with the effects of these uncertainties. Therefore, the design of a proper controller for the synchronization of chaotic systems with unknown or/and uncertain parameters is an important issue. So, in the second chapter, we addresses the modified projective synchronization between two different hyperchaotic systems in the presence of unknown or/and uncertain system parameters. Based on the Lyapunov stability theory, two control laws are proposed to make the states of two hyperchaotic systems asymptotically synchronized. Theoretical analysis and numerical simulations are shown to verify the results.Rossler chaotic system is a classic chaotic system, which has been studied throughly. However, most of the published papers only concerned on the complete synchronization, and few articles have investigated the function projective synchronization of Rossler chaotic system. Therefore, in the third chapter we discusses the function projective synchronization problem of Rossler chaotic system in the presence of known or unknown system parameters. Based on the stability theory of linear system and the Lyapunov stability theory, three sufficient conditions are proposed to make the states of two chaotic systems asymptotically synchronized. Numerical simulations are presented to show the effectiveness of the proposed schemes.In the forth chapter we first introduce a new concept of chaotic synchronization: the generalized function projective synchronization(GFPS), and then investigate the GFPS of a four-dimensional hyperchaotic system in the presence of unknown system parameters. Based on the Lyapunov stability theory a new sufficient condition is proposed to make the states of two identical hyperchaotic systems asymptotically synchronized. Numerical simulations are presented to show the effectiveness of the proposed schemes.In the fifth chapter, the research work of this thesis is summarized and the possible direction is further proposed.