1 Tianjin Key Laboratory For Control Theory & Applications in Complicated Systems, Tianjin University of Technology, Tianjin 300384, China; 2 Department of Automation, Nankai University, Tianjin 300071, China; 3 Department of Electrical and Mining Engineering, University of South Africa, Florida 1710, South Africa
Abstract 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.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61502340 and 61374169), the Application Base and Frontier Technology Research Project of Tianjin, China (Grant No. 15JCYBJC51800), and the South African National Research Foundation Incentive Grants (Grant No. 81705).
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