Simplify The Lorenz System Circuit Design And Realization Of Research

Along with the application of the chaotic theory to communication, how to generate chaotic signals by chaotic circuit systems has been received wide attention. The implementation of chaotic systems lays an important foundation for chaos application. In this thesis, chaotic analog circuit and chaotic digital circuit were designed and experimented by taking the simplified Lorenz system as the model. Research results are valuable and significant for chaos study and its application further.Adopting the discrete components, an chaotic analog circuit of simplified Lorenz chaotic system was designed. Chaotic behaviors of the simplified Lorenz system were analyzed and discussed numerically by phase maps. The system parameters correspond with the circuit element parameters. By regulating the variable resistor in the circuit, dynamic behaviors, including limit cycle, pitchfork bifurcation, period-doubling bifurcation, chaos, and the route to chaos by period-doubling bifurcation, were observed. It shows that the simplified Lorenz system has physical implementation, rich dynamic characteristics. Results from circuit experiments, theoretical analysis, and simulations are accordant.The fractional-order simplified Lorenz chaotic analog circuit system was designed and experimented by using fractional-order integral unit equivalent circuit. The necessary condition for the existence of chaos in the fractional-order simplified Lorenz system was deduced. It was found that the lowest order of this system is 2.765. The chaotic range of the fractional-order simplified Lorenz system were determined, and the chaotic behaviors of this system were analyzed.Based on FPGA technology, the simplified Lorenz chaotic digital circuit system was investigated by discretizing the continuous chaotic system. System Generator of Simulink was employed to carry on the model of discretized continuous chaotic systems, and transform it into hardware description language-VHDL. Circuit was synthesized and simulated by the ISE software developed by Xilinx. It lays a foundation for the design of the chaos pseudo-random sequence generator.