Nonlinear Dynamics

, Volume 83, Issue 1–2, pp 623–630 | Cite as

Topological horseshoe analysis on a four-wing chaotic attractor and its FPGA implement

  • Enzeng Dong
  • Zhihan Liang
  • Shengzhi Du
  • Zengqiang Chen
Original Paper


For a three-dimensional autonomous four-wing chaotic attractor, this paper rigorously verifies its chaotic properties by using topological horseshoe theory and numerical calculations. Firstly, an appropriate Poincaré section of the chaotic attractor is selected by numerical analysis. Accordingly, a certain first return Poincaré map is defined in the Poincaré section. Thereafter, by utilizing numerical calculations and topological horseshoe theory, a one-dimensional tensile topological horseshoe in the Poincaré section is discovered, which revealed that the four-wing attractor has a positive topological entropy, and verifies the existence of chaos in this four-wing attractor. Finally, by using a FPGA chip, the four-wing chaotic attractor was physically implemented, which is more suitable for engineering applications.


Chaos Poincaré map Topological horseshoe Topological entropy Chaotic circuit 



This work was partially supported by the Natural Science Foundation of China under Grant Nos. 61203138 and 61374169, the Development of Science and Technology Foundation of the Higher Education Institutions of Tianjin under Grant No. 20120829, the Science and Technology Talent and Technology Innovation Foundation of Tianjin, China, Grant No. 20130830, the Second Level Candidates of 131 Innovative Talents Training Project of Tianjin, China, Grant No. 20130115.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Enzeng Dong
    • 1
  • Zhihan Liang
    • 1
  • Shengzhi Du
    • 2
  • Zengqiang Chen
    • 3
  1. 1.Tianjin Key Laboratory For Control Theory and Applications in Complicated SystemsTianjin University of TechnologyTianjinChina
  2. 2.Department of Mechanical EngineeringTshwane University of TechnologyPretoriaSouth Africa
  3. 3.Department of AutomationNankai UniversityTianjinChina

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