Localized Approaches for Nonlinear Analysis of Chaotic Systems in Multidimensional Phase Space

In this paper, we develop algorithms for calculation of fractal measures and characteristic exponents for modeling of chaotic systems evolution. Using temporal localization along phase trajectories of a chaotic attractor reconstructed from nonlinear time series, we achieve the essential reduction of required computer resources that allows the nonlinear analysis algorithms to be realized even for higher-dimensional cases and provides their robustness to enlarging the length of time series. The numerical simulations confirm reliability of the developed algorithms and their high efficiency at calculation of fractal dimension.