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Open AccessArticle

Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System

by Shaobo He 1, Kehui Sun 1,2,* and Huihai Wang 1
1
School of Physics and Electronics, Central South University Changsha, Changsha 410083, China
2
School of Physics Science and Technology, Xinjiang University, Urumqi 830046, China
*
Author to whom correspondence should be addressed.
Academic Editors: J. A. Tenreiro Machado and António M. Lopes
Entropy 2015, 17(12), 8299-8311; https://doi.org/10.3390/e17127882
Received: 31 July 2015 / Revised: 15 December 2015 / Accepted: 16 December 2015 / Published: 18 December 2015
(This article belongs to the Special Issue Complex and Fractional Dynamics)
The fractional-order hyperchaotic Lorenz system is solved as a discrete map by applying the Adomian decomposition method (ADM). Lyapunov Characteristic Exponents (LCEs) of this system are calculated according to this deduced discrete map. Complexity of this system versus parameters are analyzed by LCEs, bifurcation diagrams, phase portraits, complexity algorithms. Results show that this system has rich dynamical behaviors. Chaos and hyperchaos can be generated by decreasing fractional order q in this system. It also shows that the system is more complex when q takes smaller values. SE and C 0 complexity algorithms provide a parameter choice criteria for practice applications of fractional-order chaotic systems. The fractional-order system is implemented by digital signal processor (DSP), and a pseudo-random bit generator is designed based on the implemented system, which passes the NIST test successfully. View Full-Text
Keywords: Fractional-order calculus; Adomian decomposition method; Complexity; Lorenz Hyperchaotic system; DSP Fractional-order calculus; Adomian decomposition method; Complexity; Lorenz Hyperchaotic system; DSP
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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.

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