Topological horseshoe analysis and field-programmable gate array implementation of a fractional-order four-wing chaotic attractor

We present a fractional-order three-dimensional chaotic system, which can generate four-wing chaotic attractor. Dynamics of the fractional-order system is investigated by numerical simulations. To rigorously verify the chaos properties of this system, the existence of horseshoe in the four-wing attractor is presented. Firstly, a Poincaré section is selected properly, and a first-return Poincaré map is established. Then, a one-dimensional tensile horseshoe is discovered, which verifies the chaos existence of the system in mathematical view. Finally, the fractional-order chaotic attractor is implemented physically with a field-programmable gate array (FPGA) chip, which is useful in further engineering applications of information encryption and secure communications.