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

中国物理B ›› 2018, Vol. 27 ›› Issue (1): 10503-010503.doi: 10.1088/1674-1056/27/1/010503

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

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)

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

收稿日期:2017-09-20 修回日期:2017-10-16 出版日期:2018-01-05 发布日期:2018-01-05
通讯作者: En-Zeng Dong E-mail:dongenzeng@163.com
基金资助:
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).

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

En-Zeng Dong(董恩增)¹, Zhen Wang(王震)¹, Xiao Yu(于晓)¹, Zeng-Qiang Chen(陈增强)², Zeng-Hui Wang(王增会)³

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

Received:2017-09-20 Revised:2017-10-16 Online:2018-01-05 Published:2018-01-05
Contact: En-Zeng Dong E-mail:dongenzeng@163.com
Supported by:
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).

摘要/Abstract

摘要： 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.

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

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.

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

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Gg (Control of chaos, applications of chaos) 05.45.Pq (Numerical simulations of chaotic systems)

董恩增, 王震, 于晓, 陈增强, 王增会. Topological horseshoe analysis and field-programmable gate array implementation of a fractional-order four-wing chaotic attractor[J]. 中国物理B, 2018, 27(1): 10503-010503.

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[J]. Chin. Phys. B, 2018, 27(1): 10503-010503.

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

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

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