中国物理B ›› 2008, Vol. 17 ›› Issue (11): 4039-4046.doi: 10.1088/1674-1056/17/11/017

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A new hyperchaotic system and its linear feedback control

蔡国梁, 郑 松, 田立新   

  1. Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang 212013, China
  • 收稿日期:2008-04-02 修回日期:2008-04-12 出版日期:2008-11-20 发布日期:2008-11-20
  • 基金资助:
    Project supported by the National Natural Science Foundations of China (Grant Nos 70571030 and 90610031) and the Advanced Talents' Foundation of Jiangsu University of China (Grant No 07JDG054).

A new hyperchaotic system and its linear feedback control

Cai Guo-Liang (蔡国梁), Zheng Song (郑松), Tian Li-Xin (田立新)   

  1. Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang 212013, China
  • Received:2008-04-02 Revised:2008-04-12 Online:2008-11-20 Published:2008-11-20
  • Supported by:
    Project supported by the National Natural Science Foundations of China (Grant Nos 70571030 and 90610031) and the Advanced Talents' Foundation of Jiangsu University of China (Grant No 07JDG054).

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摘要： This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter $k$. Furthermore，effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.

关键词: hyperchaos, linear feedback control, Lyapunov exponents, bifurcation

Abstract: This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter $k$. Furthermore，effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results.

Key words: hyperchaos, linear feedback control, Lyapunov exponents, bifurcation

中图分类号:  (Control of chaos, applications of chaos)

  • 05.45.Gg
02.30.Oz (Bifurcation theory) 05.45.Pq (Numerical simulations of chaotic systems)