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Noise perturbed generalized Mandelbrot sets. (English) Zbl 1143.37039

Summary: Adopting the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing, in this paper on the structure characteristics and the discontinuity evolution law of the additive noise perturbed generalized Mandelbrot sets (M-sets) was studied. On the influence of stochastic perturbed parameters of the structure of generalized M-sets was analyzed. The physical meaning of the additive noise perturbed generalized M-sets was expounded.

MSC:

37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations (MSC2010)
28A80 Fractals
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