中国物理B ›› 2009, Vol. 18 ›› Issue (6): 2168-2175.doi: 10.1088/1674-1056/18/6/010

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Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control

罗明伟1, 梁亦龙2, 罗小华3, 周围3, 李锐3   

  1. (1)College of Automation, Chongqing University of Posts and Telecom, Chongqing 400065, China; (2)College of Biological Information, Chongqing University of Posts and Telecom, Chongqing 400065, China; (3)College of Communication and Information Engineering, Chongqing University of Posts and Telecom, Chongqing 400065, China
  • 收稿日期:2008-11-22 修回日期:2009-01-05 出版日期:2009-06-20 发布日期:2009-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60572089) and the Natural Science Foundation of Chongqing (Grant No CSTC, 2008BB2087).

Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control

Luo Xiao-Hua(罗小华)a)†, Zhou Wei(周围)a), Li Rui(李锐)a), Liang Yi-Long(梁亦龙)b), and Luo Ming-Wei(罗明伟)c)   

  1. a College of Communication and Information Engineering, Chongqing University of Posts and Telecom, Chongqing 400065, China; b College of Biological Information, Chongqing University of Posts and Telecom, Chongqing 400065, China; c College of Automation, Chongqing University of Posts and Telecom, Chongqing 400065, China
  • Received:2008-11-22 Revised:2009-01-05 Online:2009-06-20 Published:2009-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60572089) and the Natural Science Foundation of Chongqing (Grant No CSTC, 2008BB2087).

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摘要： Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.

关键词: Liu chaotic system, Liu hyperchaotic system, nonautonomous system, synchronization control

Abstract: Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.

Key words: Liu chaotic system, Liu hyperchaotic system, nonautonomous system, synchronization control

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.45.Gg (Control of chaos, applications of chaos) 05.45.Jn (High-dimensional chaos)