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.