The autocorrelation function of the logistic map chaotic signal in relation with the statistical independence issue

The paper contributes to the complex theoretical characterization of a chaotic system. Thus, it brings together experimentally the following theoretical aspects: the statistical autocorrelation function of the chaotic system, the independence distance for extracting independent samples and the sensitivity of the chaotic system to the control parameter. The study is illustrated on the logistic map, one of the simplest chaotic systems also used in cryptography. It is presented a mean test which is applied on the autocorrelation function of the logistic map, test designed in a previous study for the tent map chaotic system. A Monte Carlo analysis is performed to highlight the results obtained.