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一个新的超混沌系统及其线性反馈同步


□ 李春彪 刘保彬 郑晓晨

  摘 要:绝对值项的非线性化作用往往可以代替平方项,Liu等人提出的类Lorenz系统中平方项用绝对值代替,并利用合适的反馈控制手段,可以构造一种新的含有绝对值项的超混沌系统。利用相图、Lyapunov指数、庞加莱映射与频谱分析等手段,证明了该系统是超混沌系统。利用线性反馈同步控制理论实现了新构造的超混沌系统的同步。数值仿真证明,只要选择合适的线性反馈控制增益矢量,就可以容易地实现驱动系统与响应系统之间的快速同步。

  关键词:类Lorenz系统; 超混沌系统; 庞加莱映射; 线性反馈控制; 同步

  中图分类号:TP273; O231.2文献标志码:A

  文章编号:1001-3695(2009)09-3304-03

  doi:10.3969/j.issn.1001-3695.2009.09.029

  New hyperchaotic system and its linear feedback synchronization

  LI Chun-biao1,2, LIU Bao-bin1,2, ZHENG Xiao-chen3

  (1. Dept. of Mechanical & Electrical Engineering, Jiangsu Institute of Economic & Trade Technology,Nanjing 210007, China; 2. Dept. of Electronic Technology, Jiangsu Research & Development Center of Food Safety Engineering Technology,Nanjing 210007,China; 3.University of Technology Sydney, Sydney 2007,Australia)

  Abstract:Absolute term can substitute for square term for nonlinear action, when the square term in Lorenz-like system proposed by Liu is replaced by absolute term, a new hyperchaotic system containing absolute term can be constructed by using proper feedback control method. At first, gave Lyapunov exponent, phase portrait, Poincaré mapping and spectrum analysis to verify that the system was hyperchaotic. Secondly, based on linear feedback synchronization control principle, realized synchronization control of the new hyperchaotic system, this synchronization method was simple and effective. Numerical simulation shows that as long as the proper linear feedback control parameter vector is chosen, it is easy to achieve the rapid synchronization between the driving system and response system.

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