Design of Multi-Scroll Chaotic Attractors Based on Tempered Fractional Differential Systems

We first introduce the definition of the stability of equilibrium point for the tempered fractional differential systems, and then the numerical simulation method (predictor-corrector method) is proposed in detail, which helps to numerically generate the multi scroll chaotic attractors of the carefully designed system. We control the tempered fractional differential systems by switching the stair function or hysteresis function, making the systems have the chaotic attractors with desired number of scrolls. The simulation results reveal that equilibrium points are surrounded by scrolls, and the number of reels exactly equals to the number of equilibrium points.