Journal
ENTROPY
Volume 17, Issue 12, Pages 8299-8311Publisher
MDPI AG
DOI: 10.3390/e17127882
Keywords
Fractional-order calculus; Adomian decomposition method; Complexity; Lorenz Hyperchaotic system; DSP
Categories
Funding
- National Natural Science Foundation of China [61161006, 61573383]
- Fundamental Research Funds for the Central Universities of Central South University [2014zzts010]
- SRF for ROCS, SEM
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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.
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