Multistability Analysis and Digital Circuit Implementation of a New Conformable Fractional-Order Chaotic System

Combining conformable differential definition and Adomian decomposition method (ADM) algorithm, the dynamics of a new 4-D fractional-order chaotic system was studied through numerical simulation in this paper. The dissipation of the system and the stability of the equilibrium points were analyzed. The evolution of the coexistence attractors with different parameters and orders were analyzed through the coexistence bifurcation diagrams, coexistence Lyapunov exponent spectrums and coexistence phase diagrams. In addition, the 0-1 test is used as an auxiliary method to verify the attractor status of the system. It is novel to use the attraction basin to investigate the dynamic behaviors of the system when two parameters change at the same time. Moreover, the digital signal processing (DSP) technology was used to simulate the fractional-order chaotic system on digital circuits, and the results are consistent with numerical simulation on computer. This research provides theoretical basis and guidance for the applications and teaching of fractional-order chaotic systems.