Generation of quasi-normal variables using chaotic maps.

摘要

The purpose of this project is to develop statistically sound methods for generating random samples using chaotic maps from which a Gaussian FM signal can be constructed. The random samples thus generated have a normal distribution with a prescribed mean and standard deviation. More specifically, we propose two random number generators that utilize first order or second order chaotic maps to draw Gaussian samples. The first method is based on the central limit theorem and allows us to approximate a Gaussian variable as the sum of a chaotic sequence, within a specific range. The second method is based on Von Neumann's Method and allows us to select a set of samples from a uniform distributed chaotic sequence to fit a Gaussian distribution within a specific range.; While implementing the first method we consider chaotic sequences generated via the Bernoulli, Tent, Logistic, and Quadratic maps. For the second method we only consider the Bernoulli and Tent maps. We verify that the probability density function approaches the theoretical Gaussian density and measure deviations as a mean square error. (Abstract shortened by UMI.)