| Chaos is a kind of special type of the nonlinear dynamical system. Chaos dynamical system has random-like behavior, appearing in deterministic nonlinear system. It can be widely found in nature, such as physics, chemistry, biology, geology, technical sciences, social sciences and so on. The study of hyperchaotic system is based on the development of chaotic system. Compared to chaotic system, hyperchaotic system has at least two positive Lyapunov exponents, so dynamics of such system is much more complex. Randomness and uncertainty of the system are greatly increased, so hyperchaotic system has greater value in engineering applications. It has great application significance and great future to design, implement and analyze hyperchaotic systems.Taking hyperchaotic system as objects, the main contents of this dissertation contain the analysis on generation, hardware implementation, synchronization and of new hyperchaotic systems. The main content is depicted as follows:(1) The origin, definition, development, basic characteristic and analysis methods of chaotic and hyperchaotic systems are recommended. Basic meanings and concepts of chaos, hyperchaos control and synchronization has also been mentioned.(2) Two new hyperchaotic systems are formulated by introducing a linear state feedback controller into two chaotic systems. The existence of the hyperchaos is not only demonstrated by Matlab simulations but also verified with Lyapunov exponents, bifurcation, Poincare mapping and power spectrum analysis.(3) New hyperchaotic systems are implemented via an electronic circuit. Different motions are observed by changing corresponding resistance. Experiment results show good consistence with the simulation results. Hyperchaotic circuit designed here has a simple structure as well as plenty kinds of dynamical behaviour, the parameters of it can also be easily debugged.(4) The adaptive synchronization which can realize the synchronization and parameters identification and globally synchronization of new hypercaotic systems is studied. The effectiveness of these controllers is demonstrated by theoretical analysis and numerical simulations. It has great foundations for applications of hyperchaos system in secure communication. |
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