Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (1): 10502-010502.doi: 10.1088/1674-1056/22/1/010502

• GENERAL • 上一篇    下一篇

Feedback control and synchronization of Mandelbrot sets

张永平   

  1. School of Mathematics and Statistics, Shandong University, Weihai 264209, China
  • 收稿日期:2012-08-29 修回日期:2012-09-26 出版日期:2012-12-01 发布日期:2012-12-01
  • 基金资助:
    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).

Feedback control and synchronization of Mandelbrot sets

Zhang Yong-Ping (张永平)   

  1. School of Mathematics and Statistics, Shandong University, Weihai 264209, China
  • Received:2012-08-29 Revised:2012-09-26 Online:2012-12-01 Published:2012-12-01
  • Contact: Zhang Yong-Ping E-mail:ypzhangsd@126.com
  • Supported by:
    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).

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摘要： 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.

关键词: Mandelbrot set, feedback control, synchronization

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.

Key words: Mandelbrot set, feedback control, synchronization

中图分类号:  (Fractals)

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