Research On Chaos Control, Chaos Synchronization And Chaos Encryption

Nonlinear science is a foundational discipline which concerns the common properties of nonlinear phenomena. Particularly, Chaos theory is one of important subdiscipline of nonlinear science. The research has studied the relative problems of chaos control, chaos synchronization and its application in cryptography using the methods of theoretical derivation and numerical simulation. The main originality in this paper can be summarized as follows:Chaos synchronization and parameters identification problem of two Chen systems is studied. Based on the Lyapunov stability theory, we design the controller which can make the states of the drive system and the response system with unknown system parameters asymptotically synchronized, and identify the system parameters. A new method improving the Lyapunov function of error dynamic of synchronization designed by Jiang and Huang et al. overcomes the limitation of the Lyapunov function having only one form. And the synchronization of two identical systems (two identical hyperchaotic Chen systems) and two different chaotic systems (the hyperchaotic Chen system and the hyperchaotic RQssler system) is achieved.A new modified coupled dynamos system is proposed firstly. The chaotic features of the modified coupled dynamos system are analyzed. The problem of control chaotic behavior of the modified coupled dynamos system is studied. Two different methods, i.e. feedback (one feedback and two feedbacks) and non-feedback methods are used to control chaos in the modified coupled dynamos system. Chaos synchronization of the modified coupled dynamos system is investigated. Three different methods, i.e. feedback, activate control and global synchronization methods are applied in this study. Based on the Lyapunov stability theory, active control technique and Gerschgorin theorem, the sufficient conditions for achieving synchronization of two identical modified coupled dynamos systems are derived.The problem of hyperchaotic Rossler system tracking control is discussed. A controller based on the reference signal is designed. The controller can not only make the Rossler system track any reference signal fast, but can make the hyperchaotic Rossler system synchronize with identical or different chaotic systems.A systematic design procedure to anti-synchronize a class of chaotic systems based on techniques from the state observer design and the pole placement technique is presented. In contrast to the conventional anti-synchronization approaches, the proposed method is rathersimple and convenient to realize anti-synchronization. Furthermore, the rate of achieving anti-synchronization is very fast.A new block encryption algorithm using multiple one-dimension chaotic maps and active S-boxes is proposed. The crypto-analysis of this algorithm has also been given in this paper. We contrast the proposed cryptosystem with Kocarev's algorithm. The preliminary experimental result about the number of S-box encrypting the plaintext for optimum effect is presented.In the studies above, one paper has been accepted by Chaos, one published and four accepted by Acta Physica Sinica, and one accepted by Chinese Journal of Control Theory and Application.