中国物理B ›› 2009, Vol. 18 ›› Issue (7): 2680-2689.doi: 10.1088/1674-1056/18/7/010

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A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system

陈增强1, 袁著祉1, 董恩增2, 陈在平2   

  1. (1)Department of Automation, Nankai University, Tianjin 300071, China; (2)Department of Automation, Tianjin University of Technology, Tianjin 300484, China
  • 收稿日期:2008-12-12 修回日期:2009-03-16 出版日期:2009-07-20 发布日期:2009-07-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China(Grant Nos 60774088 and 10772135), the Foundation of the Application Base and Frontier Technology Research Project of Tianjin, China (Grant Nos 07JCZDJC09600, 08JCZDJC21900 and 08JCZDJC18600) and the Tianjin Key Laboratory for Control Theory \& Applications in Complicated Industry Systems of China.

A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system

Dong En-Zeng(董恩增)a)† , Chen Zai-Ping(陈在平)a), Chen Zeng-Qiang(陈增强)b), and Yuan Zhu-Zhi(袁著祉)b)   

  1. a Department of Automation, Tianjin University of Technology, Tianjin 300484, China; b Department of Automation, Nankai University, Tianjin 300071, China
  • Received:2008-12-12 Revised:2009-03-16 Online:2009-07-20 Published:2009-07-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China(Grant Nos 60774088 and 10772135), the Foundation of the Application Base and Frontier Technology Research Project of Tianjin, China (Grant Nos 07JCZDJC09600, 08JCZDJC21900 and 08JCZDJC18600) and the Tianjin Key Laboratory for Control Theory \& Applications in Complicated Industry Systems of China.

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摘要： This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms, and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis, the Hopf bifurcation processes are proved to arise at certain equilibrium points. Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours; the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally, an analog electronic circuit is designed to physically realize the chaotic system; the existence of four-wing chaotic attractor is verified by the analog circuit realization.

Abstract: This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms, and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis, the Hopf bifurcation processes are proved to arise at certain equilibrium points. Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours; the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally, an analog electronic circuit is designed to physically realize the chaotic system; the existence of four-wing chaotic attractor is verified by the analog circuit realization.

Key words: chaos, four-wing chaotic attractor, bifurcation analysis, chaotic circuit

中图分类号:  (Numerical simulations of chaotic systems)

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