Hyperchaotic System Digital Circuit Design And Simulation

In this paper, research of hyper-chaotic/time delay chaotic system is carried out in the following areas:(1) The theory analysis of typical four-dimensional hyper-chaotic systems is presented. The stability of systems at the equilibrium point is analyzed according to Routh-Hurwitz criterion, The Lyapunov Exponents of the systems are calculated either. Further analysis of the system dynamical behavior is described with variable parameter. At the mean time, the auxiliary explicit of power spectral characteristics identified the existence of chaotic attractors. With input of time delays, the dynamic behaviors of these systems are under further observation. The comparative dynamical analyses of the two Lorenz-classed systems have got a certain theoretical value and practical significance.(2) A Four-Dimensional chaotic system based on Lorenz system is designed by linear feedback expansion. Dynamic characteristics of the system are analyzed. Dynamics of the system have been further studied after the introduction of time delays. Chaotic system by analog circuit design is sensitive to component deviations and environmental impact. The chaotic system is discretized prior to overcome the inherent shortcomings of analog circuit. A method of designing chaotic attractor based on DSP Builder is presented. By optimized digital circuit design and rational configuration of parameters, the signal amplitude is reasonably controlled while with jagged trajectories. In computer simulations, results by DSP Builder are basically consistent with results of Matlab.(3) As Hyper-chaotic L u&& system to be studied, influence of the sampling frequency to dynamics of the discrete chaotic ones is analyzed of proposal. The L u&& system being processed by majorized first order differential equations prior, a hyper-chaotic digital circuit based on DSP Builder is presented in order to overcome such defects. By optimizing the design of sampling frequency selection, gain adjustments, parameter configurations etc., and the hyper-chaotic circuit runs stably while the signal amplitude is reasonably controlled; curves of the digital chaotic sequence show smooth without jagged shape. The circuit can be applied to other digital realization of chaotic systems with generability and versatility. Based on hyper-chaotic digital circuits, a new variable delay controller is designed to achieve variable delay chaotic digital circuits. Operation of the circuits is desirable, generating chaotic sequences of complex variable delays. The experimental results mentioned above are fully consistent with phase space structures of the continuous chaotic system, which shows the development of chaotic systems based on FPGA is feasible and practical.