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.
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).
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