Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System
Abstract
:1. Introduction
2. Numerical Solution of the Fractional-Order Lorenz Hyperchaotic System
2.1. Adomian Decomposition Method
2.2. Fractional-Order Lorenz Hyperchaotic System
3. Dynamics Analysis of the Fractional-Order Lorenz Hyperchaotic System
3.1. Bifurcation Analysis
3.2. Observation of Chaotic Attractors
3.3. Spectral Entropy Complexity Analysis
3.4. C Complexity Analysis
4. Digital Circuit Implementation
4.1. DSP Implementation
4.2. Pseudo-Random Sequence Generator
p-Value | Proportion | Success | |
---|---|---|---|
Frequency | 0.366918 | 100% | √ |
B. Frequency | 0.002559 | 99% | √ |
C. Sums | 0.275709 | 99% | √ |
Runs | 0.048716 | 98% | √ |
Longest Run | 0.935716 | 99% | √ |
Rank | 0.883171 | 99% | √ |
FFT | 0.574903 | 100% | √ |
N.O.Temp. | 0.002203 | 97% | √ |
O.Temp. | 0.834308 | 100% | √ |
Universal | 0.759756 | 99% | √ |
App. Entropy | 0.759756 | 98% | √ |
R.Excur. | 0.005166 | 96.7% | √ |
R.Excur.V. | 0.105618 | 96.7% | √ |
Serial | 0.075719 | 99% | √ |
L. Complexity | 0.554420 | 99% | √ |
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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He, S.; Sun, K.; Wang, H. Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System. Entropy 2015, 17, 8299-8311. https://doi.org/10.3390/e17127882
He S, Sun K, Wang H. Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System. Entropy. 2015; 17(12):8299-8311. https://doi.org/10.3390/e17127882
Chicago/Turabian StyleHe, Shaobo, Kehui Sun, and Huihai Wang. 2015. "Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System" Entropy 17, no. 12: 8299-8311. https://doi.org/10.3390/e17127882