The Generation Of Hyperchaotic System And Its Synchronization

Since E. N. Lorenz discovered the first chaotic attractor, chaos theory attracted scholars in many fields working on its further research. Chaos, a kind of pseudo-random phenomenon in certain systems, widely exists in nature. Chaos signals possesses some properties including the sensitive dependence on initial conditions, unpredictability, wide frequency spectrum similar to noise, etc. with the result that it has natural concealment, which brings a brilliant development prospects in the secret communication field. However, with the gradually improvement of decoding technology, the simple chaos systems can not satisfy the development needs of communications technology. The hyperchaotic system possesses at least two positive Lyapunov exponents, so its attractor expands in more than one direction and its output is more difficult to predict. Compared to chaotic system, hyperchaotic system possesses higher randomness and complexity, which can improve the confidentiality performance of communication system. Therefore, people’s concern gradually turns to the hyperchaotic system. The generation of hyperchaotic system and its synchronous technology research are one of the subjects with research significance and development prospects extremely.The main work of this thesis is to generate the new family of Lorenz hyperchaotic system via adding a simple linear feedback controller to the family of Lorenz system based on the thinking of chaos anti-control. On this basis, the thesis has mainly studied and discussed their synchronization. The main works and innovation include the following facets:(1) Based on the principle of chaotic anti-control, a new family of Lorenz hyperchaotic system is formulated by adding a simple linear feedback controller to the family of Lorenz system in this thesis. It demonstrates that there is hyperchaotic behavior in this new system by means of detailed analysis of its dynamic characteristic including symmetry, dissipation and stability of balance point. On this basis, it provides a quantitative description of the dynamic characteristics in this family by using Lyapunov exponents. It has been confirmed that this family possesses broad and stable hyperchaotic region which makes the new family of hyperchaotic system have a good application prospect in the secure communication. (2) Based on the theory of linear feedback synchronization and drive-response synchronization, two synchronization schemes for the family of Lorenz hyperchaotic system are designed by adding two simple linear feedback controllers to the family of Lorenz system. Combing with Lyapunov stability theory, the ranges of each feedback control coefficient are determined and the effectiveness of these two kinds of proposed schemes is demonstrated. In addition, it has laid a good foundation for its application research.(3) According to the physical realization principle of continuous chaotic systems, the circuits of the new family of Lorenz hyperchaotic system and their synchronization are built, and that these circuits are implemented by using Multisim with some ideal experimental results which will provide beneficial references for further research in the secure communication.