%0 Journal Article
%T Self-similar motion for modeling anomalous diffusion and nonextensive statistical distributions
%A Zhifu Huang
%A Guozhen Su
%A Qiuping A Wang
%A Jincan Chen
%J Statistics
%D 2010
%I arXiv
%R 10.1088/1742-5468/2010/05/L05001
%X We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square displacement versus time generated here show that the motion is a kind of anomalous diffusion with the diffusion coefficient depending on the self-similar rates. In addition, it is found that the distribution of displacement agrees to a reliable precision with the q-Gaussian type distribution in some cases and bimodal distribution in some other cases. The results obtained show that the self-similar motion may be used to describe the anomalous diffusion and nonextensive statistical distributions.
%U http://arxiv.org/abs/1001.2880v1