Generating Multi-Scroll Chaotic Attractors via Switched Fractional Systems

A method is presented to generate multi-scroll chaotic attractors by switched fractional systems. Two sub-models in this structure are constructed by different piecewise-linear functions. It is proved that the switched systems can demonstrate multi-scroll chaotic attractors with suitable parameters and switching rule. Moreover, in order to obtain the multi-scroll chaotic attractors with the lowest system order, the relationship between Lyapunov exponents and parameters is studied. It is found that the multi-scroll chaotic attractors can be presented with a system order larger than 0.9. Numerical examples are provided to illustrate the effectiveness of the proposed scheme.