Copyright © 2012 Wang Xingyuan and Qin Xue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We, for the first time, investigate the basic behaviours of a chaotic switching fractional system via both theoretical and numerical ways. To deeply understand the mechanism of the chaos generation, we also analyse the parameterization of the switching fractional system and the dynamics of the system's trajectory. Then we try to write down some detailed rules for designing chaotic or chaos-like systems by switching fractional systems, which can be used in the future application. At last, for the first time, we proposed a new switching fractional system, which can generate three attractors with the positive largest Lyapunov exponent.