Applied statistical analysis for strange attractors and related problems

Nowadays, the number of chaos applications has grown considerably. The applied theory of chaotic dynamic systems requires new tools for its statistical analysis. In this paper the so-called "model distribution" approach based on the cumulants and their equations is presented in order to obtain a statistical characterization of the chaos generated by differentiable dynamic systems; as examples, the Lorenz and Chua attractors are considered. The fractional analysis of system dynamics is considered as well.