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

doi:10.1088/1674-1056/27/1/010503

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.

Keywords: fractional-order chaotic system Poincaré map topological horseshoe field-programmable gate array (FPGA)

Received: 20 September 2017
Revised: 16 October 2017
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Gg	(Control of chaos, applications of chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)

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).

Corresponding Authors: En-Zeng Dong
E-mail: dongenzeng@163.com

Cite this article:

En-Zeng Dong(董恩增), Zhen Wang(王震), Xiao Yu(于晓), Zeng-Qiang Chen(陈增强), Zeng-Hui Wang(王增会) Topological horseshoe analysis and field-programmable gate array implementation of a fractional-order four-wing chaotic attractor 2018 Chin. Phys. B 27 010503

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

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