Theoretical and experimental analysis of regularities of autocorrelation function decay of the Lorentz attractor

摘要

In the present paper statistical properties of the Lorentz attractor are studied and general regularities of the temporal behavior of the autocorrelation function are determined. Using a symbolic dynamics the character of a random process of switchings between two symmetric areas of the attractor is investigated. It is shown that this process posseses the statistic of a telegraphic signal with a non Poisson distribution of impulses duration. It is demonstrated that the ACF of the Lorentz attractor decays with the linear law on small times. The theoretical and numerical results are compared with data of physical experimental data.