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

摘要

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