Feedback control and synchronization of Mandelbrot sets

doi:10.1088/1674-1056/22/1/010502

Abstract The movement of the particle could be depicted by Mandelbrot set from the viewpoint of fractal. According to the requirement, the movement of the particle needs to show different behaviors. In this paper, the feedback control method is taken on the classical Mandelbrot set. By amending the feedback item in the controller, the control method is applied to the generalized Mandelbrot set. And by taking the reference item to be the trajectory of another system, the synchronization of Mandelbrot sets is achieved.

Keywords: Mandelbrot set feedback control synchronization

Received: 29 August 2012
Revised: 26 September 2012
Accepted manuscript online:

PACS:	05.45.Df	(Fractals)
	05.45.Gg	(Control of chaos, applications of chaos)
	05.45.Xt	(Synchronization; coupled oscillators)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10971120), the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2010FM010 and ZR2011FQ035), and the Independent Innovation Foundation of Shandong University, China (Grant No. 2011ZRYQ012).

Corresponding Authors: Zhang Yong-Ping
E-mail: ypzhangsd@126.com

Cite this article:

Zhang Yong-Ping (张永平) Feedback control and synchronization of Mandelbrot sets 2013 Chin. Phys. B 22 010502

[1]	Osbaldestin A H 1995 J. Phys. A Math. Gen. 28 5951
[2]	Hu B and Lin B 1989 Phys. Rev. A 39 4789
[3]	Christian Beck 1999 Physica D 125 171
[4]	Wang X Y and Meng Q Y 2004 Acta Phys. Sin. 53 388 (in Chinese)
[5]	Liu S T and Zhang Y P 2008 Acta Phys. Sin. 57 737 (in Chinese)
[6]	Zhang Y P and Liu S T 2008 Chin. Phys. B 17 543
[7]	Zhang Y P, Sun W H and Liu C A 2010 Chin. Phys. B 19 050512
[8]	Yuen C H and Wong K W 2012 Chin. Phys. B 21 010502
[9]	Wand X Q, Ma J, Zhang X H and Wang X G 2011Chin. Phys. B 20 050510
[10]	Duan D H, Xu W, Su J and Zhou B C 2011 Chin. Phys. B 20 030501
[11]	Gao T F, Liu F S and Chen J C 2012 Chin. Phys. B 21 020502
[12]	Ye Z Y, Yang G and Deng C B 2011Chin. Phys. B 20 010207
[13]	Ott E, Grebogi C and Yorke Y A 1990 Phys. Rev. Lett. 64 1196
[14]	Michael E Brandt and Chen G 1997 IEEE Trans. Cir. Sys. I 44 1031

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