中国物理B ›› 2010, Vol. 19 ›› Issue (5): 50512-050512.doi: 10.1088/1674-1056/19/5/050512

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Control and synchronization of second Julia sets

孙伟华1, 刘长安1, 张永平2   

  1. (1)School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, China; (2)School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, Chinap;School of Control Science and Engineering, Shandong University, Jinan 250061, China
  • 收稿日期:2009-09-10 修回日期:2009-10-25 出版日期:2010-05-15 发布日期:2010-05-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos.~60874009 and 10971120) and a foundation for the author of National Excellent Doctoral Dissertation of China (FANEDD) (Grant No.~200444).

Control and synchronization of second Julia sets

Zhang Yong-Ping(张永平)a)b)†, Sun Wei-Hua(孙伟华)a), and Liu Chang-An(刘长安) b)   

  1. a School of Mathematics and Statistics, Shandong University at Weihai, Weihai 264209, China; b School of Control Science and Engineering, Shandong University, Jinan 250061, China
  • Received:2009-09-10 Revised:2009-10-25 Online:2010-05-15 Published:2010-05-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos.~60874009 and 10971120) and a foundation for the author of National Excellent Doctoral Dissertation of China (FANEDD) (Grant No.~200444).

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摘要： A visualization of Julia sets of the complex Henon map system with two complex variables is introduced in this paper. With this method, the optimal control function method is introduced to this system and the control and synchronization of its Julia sets are achieved. Control and synchronization of generalized Julia sets are also achieved with this optimal control method. The simulations illustrate the efficacy of this method.

Abstract: A visualization of Julia sets of the complex Henon map system with two complex variables is introduced in this paper. With this method, the optimal control function method is introduced to this system and the control and synchronization of its Julia sets are achieved. Control and synchronization of generalized Julia sets are also achieved with this optimal control method. The simulations illustrate the efficacy of this method.

Key words: Henon map, Julia set, optimal control, synchronization

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

  • 05.45.Gg
05.45.Xt (Synchronization; coupled oscillators) 02.30.Uu (Integral transforms) 02.30.Yy (Control theory) 02.10.Ab (Logic and set theory)