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.
Received: 15 May 2007
Revised: 31 May 2007
Accepted manuscript online:
Fund: 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).
Cite this article:
Zhang Yong-Ping(张永平) and Liu Shu-Tang(刘树堂) Gradient control and synchronization of Julia sets 2008 Chin. Phys. B 17 543
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