| Chaos is a kind of special complicated nonlinear systems, since it has the characteristics of sensitivity to initial values and high randomicity, which attracts great attentions from investigators. Chaos is ubiquitous in the nature, and it has been universally applied in various fields such as biology, physics, chemistry, engineering and information. Since1990s, chaotic synchronization phenomena have been observed in more and more domains. Chaotic synchronization has been developed very quickly as an important research field in chaotic science, and much progress has been gotten in its applications such as secret communication and image manipulation. This thesis focuses on the chaotic secret communication based on the current research results, and the multi-node chaotic synchronization problem is studied in the secret communication system. The problems of finite-time synchronization control and bidirectional coupled synchronization control of chaotic systems are studied under the above background. The main contents are as follows:Firstly, some important background knowledge about chaos is introduced in this thesis, including the origin and development of chaotic theory, the current research results of chaotic synchronization, and its applications in the secret communication. Furthermore, the definition, the feature, the Lyapunov exponent of chaos and several kinds of typical chaotic systems are introduced. These are the foundations for the further studying of chaotic control and chaotic synchronization.Secondly, various methods and types of chaotic synchronization are summarized. The finite-time stability theory of the nonlinear systems is used for the chaotic synchronization, then the finite time synchronization control laws are proposed, and also two controllers are designed to achieve the finite time synchronization for two chaotic systems. Based on the finite-time stability theory, two kinds of stability conditions of error system are proposed to achieve the finite-time synchronization. The numerical simulation results verify the effectiveness of the proposed schemes.Finally, the problem of the bidirectional coupled synchronization of Lorenz system is investigated. Then, the generalized projective synchronization of bidirectional coupled synchronization chaotic system is studied. Furthermore, the problem of the bidirectional coupled chaotic system which satisfies the synchronization in finite-time is discussed. The simulation results show that the error system can be stabilized and converges to the zero point with good control effect by using the Matlab software. Then, these contents are applied into the secure communication system, which achieve the chaotic synchronization between multiple nodes. |
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