中国物理B ›› 2008, Vol. 17 ›› Issue (2): 543-549.doi: 10.1088/1674-1056/17/2/032

• GENERAL • 上一篇    下一篇

Gradient control and synchronization of Julia sets

张永平, 刘树堂   

  1. School of Control Science and Engineering, Shandong University, Jinan 250061, China
  • 收稿日期:2007-05-15 修回日期:2007-05-31 出版日期:2008-02-20 发布日期:2008-02-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60472112) and a foundation for the author of National Excellent Doctoral Dissertation of China (FANEDD) (Grant No 200444).

Gradient control and synchronization of Julia sets

Zhang Yong-Ping(张永平)† and Liu Shu-Tang(刘树堂)   

  1. School of Control Science and Engineering, Shandong University, Jinan 250061, China
  • Received:2007-05-15 Revised:2007-05-31 Online:2008-02-20 Published:2008-02-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60472112) and a foundation for the author of National Excellent Doctoral Dissertation of China (FANEDD) (Grant No 200444).

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摘要： This paper firstly introduces the control methods to fractals and give the definition of synchronization of Julia sets between two different systems. Especially, the gradient control method is taken on the classic Julia sets of complex quadratic polynomial $z_{n+1}=z_n^2+c$, which realizes its Julia sets control and synchronization. The simulations illustrate the effectiveness of the method.

Abstract: This paper firstly introduces the control methods to fractals and give the definition of synchronization of Julia sets between two different systems. Especially, the gradient control method is taken on the classic Julia sets of complex quadratic polynomial $z_{n+1}=z_n^2+c$, which realizes its Julia sets control and synchronization. The simulations illustrate the effectiveness of the method.

Key words: Julia set, gradient control, synchronization

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.45.Df (Fractals) 07.05.Dz (Control systems) 02.10.De (Algebraic structures and number theory)