中国物理B ›› 2010, Vol. 19 ›› Issue (2): 20510-020510.doi: 10.1088/1674-1056/19/2/020510

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Adaptive synchronisation of fractional-order chaotic systems

杨世平1, 张若洵2   

  1. (1)College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China;Hebei Advanced Thin Films Laboratory, Shijiazhuang 050016, China; (2)College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China;Hebei Advanced Thin Films Laboratory, Shijiazhuang 050016, China;College of Elementary Education, Xingtai University, Xingtai 054001, Hebei Provin
  • 收稿日期:2009-06-30 修回日期:2009-08-19 出版日期:2010-02-15 发布日期:2010-02-15
  • 基金资助:
    Project supported by the Natural Science Foundation of Hebei Province of China (Grant No.~A2008000136).

Adaptive synchronisation of fractional-order chaotic systems

Zhang Ruo-Xun(张若洵)a)b)c) and Yang Shi-Ping(杨世平)a)b)†   

  1. a College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China; b Hebei Advanced Thin Films Laboratory, Shijiazhuang 050016, China; c College of Elementary Education, Xingtai University, Xingtai 054001, Hebei Province, China
  • Received:2009-06-30 Revised:2009-08-19 Online:2010-02-15 Published:2010-02-15
  • Supported by:
    Project supported by the Natural Science Foundation of Hebei Province of China (Grant No.~A2008000136).

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摘要： A new stability theory of nonlinear dynamic systems is proposed, and a novel adaptive synchronisation method is presented for fractional-order chaotic and hyperchaotic systems based on the theory described in this paper. In comparison with previous methods, not only is the present control scheme simple but also it employs only one control strength, converges very fast, and it is also suitable for a large class of fractional-order chaotic and hyperchaotic systems. Moreover, this scheme is analytical and simple to implement in practice. Numerical and circuit simulations are used to validate and demonstrate the effectiveness of the method.

Abstract: A new stability theory of nonlinear dynamic systems is proposed, and a novel adaptive synchronisation method is presented for fractional-order chaotic and hyperchaotic systems based on the theory described in this paper. In comparison with previous methods, not only is the present control scheme simple but also it employs only one control strength, converges very fast, and it is also suitable for a large class of fractional-order chaotic and hyperchaotic systems. Moreover, this scheme is analytical and simple to implement in practice. Numerical and circuit simulations are used to validate and demonstrate the effectiveness of the method.

Key words: new stability theory, fractional-order chaotic system, adaptive synchronisation

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.45.Gg (Control of chaos, applications of chaos)