Kehui Sun

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

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.

Dynamic analysis and implementation of a digital signal processor of a fractional-order Lorenz-Stenflo system based on the Adomian decomposition method

By adopting the Adomian decomposition method, the fractional-order Lorenz–Stenflo (LS) system is solved and implemented in a digital signal processor (DSP). The discrete iterative formula of the system is deduced, and a Lyapunov exponent spectrum algorithm is designed. The dynamics of the fractional-order LS system with sets of parameters are analyzed by means of Lyapunov exponent spectra, bifurcation diagrams and 0-1 test. The results illustrate that the fractional-order LS system has rich dynamic behaviors, and both the system parameter and the fractional order can be taken as bifurcation parameters. We implement the fractional-order LS system on a DSP platform. Phase portraits of the fractional-order LS system generated in the DSP agree well with those obtained by computer simulations. This lays a good foundation for the application of the fractional-order LS system.

Characteristic Analysis of Fractional-Order 4D Hyperchaotic Memristive Circuit

Dynamical behaviors of the 4D hyperchaotic memristive circuit are analyzed with the system parameter. Based on the definitions of fractional-order differential and Adomian decomposition algorithm, the numerical solution of fractional-order 4D hyperchaotic memristive circuit is investigated. The distribution of stable and unstable regions of the fractional-order 4D hyperchaotic memristive circuit is determined, and dynamical characteristics are studied by phase portraits, Lyapunov exponents spectrum, and bifurcation diagram. Complexities are calculated by employing the spectral entropy (SE) algorithm and C0 algorithm. Complexity results are consistent with that of the bifurcation diagrams, and this means that complexity can also reflect the dynamic characteristics of a chaotic system. Results of this paper provide a theoretical and experimental basis for the application of fractional-order 4D hyperchaotic memristive circuit in the field of encryption and secure communication.