Cumulant Analysis of Rössler Attractor and its Applications

This paper is dedicated to the statistical analysis of the chaos, generated by Rössler attractor, based on the socalled “Degenerated Cumulant Equations” method. The approach is illustrated by the calculus of the first cumulants, which are necessary to create an approximation of the Probability Density Function (PDF), applying the Gramm-Charlier series, the model distribution method, etc. An approximate method for the variance calculation at the output of the Rössler strange attractor is presented as well. The latter is based on the Kolmogorov-Sinai entropy estimated by the Lyapunov exponents for a statistically linearized chaotic system. Finally, an application using Rössler attractor output signals to model Radio Frequency Interferences (RFI) provided by Peripherical Component Interface express (PCIe) serial bus of high speed interconnects of Laptops and Desktops is presented.