An experimental synthesis methodology of fractional-order chaotic attractors

Abstract

A novel synthesis methodology of fractional-order chaotic systems, from the level of nonlinear systems until their experimental verification using microcontrollers, is presented. Firstly, the integer-order behavioral model of the Lorenz’s, Rossler’s, Chen’s, Liu’s, Saturated Nonlinear Function Series at one- and two-direction systems is briefly reviewed. Secondly, a first-order transfer function that approximates the behavior of a fractional-order integrator, based on continued fraction expansion method, is substituting the integer-order integrator inside the revised previously chaotic systems. Thirdly, the minimum phase Al-Alaoui’s transformation method is used for synthesizing all fractional-order chaotic systems in the discrete domain and are programmed in MATLAB and in the Arduino DUE development board. For a fair comparison, the minimum phase Al-Alaoui’s algorithm not only is used for solving the integer-order chaotic systems and it is also programmed in MATLAB and Arduino DUE board, but same initial conditions are also used for both interger- and fractional-order chaotic systems. Finally, experimental results of the integer- and fractional-order chaotic oscillators are shown. The results obtained not only allow a simple synthesis methodology of fractional-order chaotic attractors and their experimental evidence on reconfigurable hardware, but also demonstrate the viability of fractional attractors to be used in various applications such as secure communications, robot control, cryptography and so on.