Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors

Several efforts have been recently devoted to the hardware implementations of fractional systems. This manuscript makes a contribution to the topic by introducing the first example of hardware implementation of a 2D fractional map with hidden. Specifically, the paper presents first a new class of two-dimensional fractional map with no equilibruim points using the Grunwald-Letnikov difference operator. Then, the system dynamics are analyzed via numerical simulation, such as bifurcation diagrams, Lyapunov exponents and phase portraits. Finally, the paper illustrates a hardware implementation of the 2D fractional map via a microcontroller, with the aim to show the real presence of chaotic hidden attractors in physical systems described by non-integer order maps.