Hardware Implementation of a Two-dimensional Fractional Map with Hidden Attractors
Adel Ouannas, Amina–Aicha Khennaoui, Giuseppe Grassi, Viet–Thanh Pham, Zohir Dibi, Shaher Momani
Abstract
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.