Analysis Chaotic Sequence Characteristics And The FPGA Implementation Based On Chebyshev Polynomial

Chaos is the inherent uncertainties system which is under action of the time to produce macro complex phenomenon. Its theoretical system is study nonlinear system stochastic of nature which is the laws of Science. Chaos has strong sensitivity to the initial conditions, the good correlation, run-length feature and balance characteristics, etc. which makes it have extensive application in the field of spread spectrum communication space.From the initial value sensitivity, fixed point and periodic point of chaotic systems to analyze the mechanism of chaos, we have to consider the accuracy problem of the computer. We found that the influence of the calculation precision can lead to some do not tally with the theory of the expected results. Specifically, in two aspects:Frstly there exist errors between the computer simulation of chaotic orbit and the theory of orbital. Secondly, because of the influence of the calculation precision, after many iterations chaotic dynamics characteristics of the chaotic system is reduced, leading to generate chaos sequence periodic cycle.This paper analyses the error effect on chaotic orbits. The error is affected by the precision of computer. Although the error of the nonlinear system can lead to numerical deviation, but it is not as the linear system of the error, with the increase of the number of iterations, error will increase. The error of the chaotic system is still within the scope of the whole system and presents a random distribution in the bound system. It is because of this phenomenon, we can through the computer simulation to realize and analog chaotic.This paper puts forward a way of adding random disturbance to solve after affected by the precision of Chebyshev chaotic mapping which produces periodic sequence problem. Because the computer default calculation is to exceed precision decimal taken a round of the regularity of interception of, so take the way of random disturbance to break the regularity, make precision within the scope of the last decimal places more irregular and extend the aperiodic of chaos. This paper respectively from solid value sequence and bit extracting quantitative digital ways to analysis adding modifiedChebyshev maps of the disturbance of random sequence which is under the condition of single precision and its relevance, run-length feature and balance characteristics,etc. The simulation results show its the overall performance is better than without disturbance of Chebyshev maps generated sequence.Finally, this paper presents a perturbation type Chebyshev maps based on FPGA hardware implementation method, use Verilog HDL language, respectively on QurtusⅡ9.0software and hardware. DE2.implements the output of digital chaotic sequence which for its application in the field of spread spectrum communication laid the foundation.