Hyperchaotic Generalized Synchronization Control System And Its Circuit Implementation

Chaotic phenomenon is common in our real life, the research and application of thescience of chaos has penetrated the field of natural sciences and social sciences, such as:mathematics, physics, economics, communication, information technology, bio-medicine, etc.its application in the field of communications and signal processing especially value. In general,low-dimensional chaotic system structure is relatively simple, the dynamic characteristics richenough, and the dynamics of hyperchaos has more abundant and high dimensional feature,randomness and uncertainty of the system are significantly improved. Long-term unpredictableand sensitivity to initial conditions, so that the chaotic system having outstanding value in thepractical application in the field of engineering. This article mainly analysis the hyperchaossystem, the series of distinguished research from non-delay to delay and analog to digital. Themain discussion from the following several parts:(1) The generalized projective synchronization and generalized synchronization ofhyperchaotic system research. With hyperchaotic system of Chen and hyperchaotic system ofLü as the research basis, by adding a parameter variable, to expand the number of dimensions,it can design a new four-dimensional system. According to the Routh-Hurwit decision based onthe analysis of the stability of the system, and through the four-dimensional system’s Lyapunovexponent, attractor and system power spectral to analysis the dynamic characteristics, such as toverify the new characteristics of the structural system. Finally, through the combined use ofactive control and adaptive control method, respectively, to achieve the hyperchaoticgeneralized projection synchronization and generalized synchronization. The good experimentalresults show some theoretical guidance value.(2) The circuit design of the hyperchaotic system. Newly constructed four-dimensionalchaotic system by Multisim software analog circuit design, to complete the design by choosingthe appropriate parameters, and then debug the simulation results of the experiment to get theideal simulation effect. But due to the analog circuit with some deficiencies: circuit aging easily,interference by outside, resistance characteristics, and so on. On this condition use the FPGAtodesign digital circuit, by selecting module of DSP Builder reasonable design can complete digitalcircuit. DSP Builder digital circuit has incomparable advantages than analog circuit: highprecision, fast operation, field programming, susceptible to interference and so on.(3) Time-delay hyperchaotic system digital circuit design. In our reality production worksthere are many time delay phenomenon, thus proposing time-delay chaotic systems research isvery necessary. Based on the new structured hyperchaos create the time-delay hyperchaossystem by introducing only one time delay. Through basic analysis of the dynamic characteristics, shows that time delay system with super chaos characteristics, at last, Matlaband DSP Builder have been studied in simulation experiment, experimental results once againreflects the superiority of digital circuits. Also explains the FPGA used in development andutilization value of the chaotic systems.Hyperchaotic system and delay systems constructed in this paper have good dynamiccharacteristics, and according to the constructed hyperchaos synchronization problems betweenthe systems of research, obtained from circuit theory and effect, for the following hardwareintegration analysis flow, and for constructing more complex hyperchaos system researchprovides a certain basis of data analysis.