The Sensitivity of the Fractal Spectrum: a Means of Controlling the Statistical Properties of Chaotic Signals

Abstract

This paper investigates the possibility of generating pseudorandom numbers by means of non-linear circuits. We intend to demonstrate the links between the circuit elements and the chaotic properties, by defining the sensitivity of the fractal spectrum of the signal related to the elements of the circuit. In this way, the statistical properties and the ability to change them simply by an adequate adjustment of the circuit elements is made possible. To illustrate the method, a modified circuit based on the well known Wien-bridge oscillator is analysed through computer simulation. A study of the influence of the components of this circuit and their impact on the properties of the chaotic signal is also carried out, based on the newly introduced sensitivities. The study showed that not only the main statistical indicators, such as the mean, the standard deviation, the median etc., but even the type of the probability density function can be changed only by means of small variations of certain circuit elements. Ill. 13, bibl. 17, tabl. 2 (in English; abstracts in English and Lithuanian).

http://dx.doi.org/10.5755/j01.eee.114.8.688