Analysis of the chaotic maps generating different statistical distributions

4th International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Lawnik, M.^1

Faculty of Applied Mathematics, Silesian University of Technology, ul. Kaszubska 23, Gliwice

44-100, Poland^1

关键词: Chaotic map;    Cumulative distribution function;    Inverse functions;    Skew tent map;    Standard normal distributions;    Statistical distribution;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/633/1/012086/pdf
DOI  :  10.1088/1742-6596/633/1/012086

来源: IOP

【 摘 要 】

The analysis of the chaotic maps, enabling the derivation of numbers from given statistical distributions was presented. The analyzed chaotic maps are in the form xk+1= F-1(U(F(xk))), where F is the cumulative distribution function, U is the skew tent map and F-1is the inverse function of F. The analysis was presented on the example of chaotic map with the standard normal distribution in view of his computational efficiency and accuracy. On the grounds of the conducted analysis, it should be indicated that the method not always allows to generate the values from the given distribution.