Abstract
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.
Highlights
In recent years, dynamics of fractional-order chaotic systems have become a hot topic [1,2,3]
The dynamics of the fractional-order Lorenz hyperchaotic system is investigated in this paper
It is solved as a discrete map by applying Adomian Decomposition Method (ADM)
Summary
Dynamics of fractional-order chaotic systems have become a hot topic [1,2,3]. LCEs of fractional-order chaotic systems are calculated based on ADM by applying QR decomposition method [16]. SE and C0 algorithms are proper choices to estimate the complexity of a time series accurately and rapidly without any over-coarse graining preprocessing [21,22]. They are used to measure the complexity of chaotic systems [23,24] and physiological signals [25], respectively. Compared with analog circuit implementation, digital circuit realization is a more reliable and accurate way for the application of fractional-order chaotic systems.
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