| As one important branch of nonlinear science, chaos is widely used in secure communication and information cryptology for its excellent characteristics. The key technologies are the synchronization algorithms and dynamic behavior analysis of chaotic system. Based on these two aspects, the main work of this paper are as follows:(1) For a typical chaotic system with single scroll attractor structure, the self-synchronization and different structure synchronization are implemented utilizing a combined method of linear and nonlinear feedback, global synchronization method, active control method and single vector unidirectional coupling method designed by author, respectively. The effectiveness of these methods is verified by theoretical analysis and numerical simulations.(2) For the non-ideal chaotic system with parameters perturbation and external disturbance, a detailed feedback sychronization scheme is designed based on Lyapunov stability theorem. Theory proves that this method can achieve approximate synchronization of arbitrary precision between systems in the case of bounded disturbances. The introduced variable structure control method can control the error range effectively in condition of not producing vibration.(3) Impulsive synchronization of the two identical chaotic systems with different initial conditions is studied. The sufficient conditions on feedback strength and impulsive interval are established to guarantee the synchronization. The method is simple and the relevant mathematical proof is presented. Numerical simulations show the effectiveness of the method.(4) For achieving the global synchronization of a new hyperchaos system, how to design and obtain the coupled control matrix and its'comparison is discussed when either knowing or unknowing the system boundary.(5) For a new hyperchaos Lorenz system proposed by Wang et al, its fractional form is studied. Not only its the lowest orders for hyperchaos is obtained, but also a scheme without the using of Lyapunov exponent for judging the system stability is used to achieving its generalized synchronization. Both theoretical proofs and numerical simulations have verified the method's validity.(6) A new four-dimensional continuous autonomous system is constructed and its complex dynamic behavior is analyzed in detail by the way of discussing control parameters of system. Not only the new introduced control parameter can maintain excellent chaotic characters of the system in an infinite interval, but also the change of another parameter's value can expand the bound of parameter to keep the system's hyperchaos and let the system appear chaos with a new attractor again after radiation.(7) A new block chaotic cryptosystem based on Coupled Map Lattice is designed. It's mutual perturbation between coupled chaotic systems improves the dynamic degradation problem of chaotic system caused by limited precision of digital computer. The updated encryption order of the blocks dynamically by certain rule and the complex feedback association between different sub-regions make the law between plaintext and ciphertext more complex. Therefore, the security of the system is enhanced. Both experimental results and comparisons with other cryptosystems prove the proposed cryptosystem has obvious security advantages. Because the using of simple one dimensional chaotic maps, the proposed cryptosystem is more efficient and practical.The research in this paper are jointly supported by the National Natural Science Foundation of China (Nos.:60573172 and 60973152), the Superior University Doctor Subject Special Scientific Research Foundation of China (No.:20070141014) and the National Natural Science Foundation of Liaoning Province(No.:20082165). |
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