27 March 2001 Fractal and multidimensional analysis of data from delay complex systems
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The method of multifractal analysis for multidimensional attractor is proposed, the adaptive segmentation of phase trajectories is used analogously generalized correlation integral approach. A rarefied sequence of points of phase trajectory just forms the centers of segmentation cells, the upper boundary of such rarefying is estimated from statistical analysis of quasi-periodicity along phase trajectories of multidimensional attractor. This method allows to reduce a required computer time in comparison with traditional correlation integral approach and provides a good convergence. So far as the attractor reconstruction was implemented in Takens phase space, analytical approaches for product scheme of functional matrixes derived from delay differential iterations is developed for such phase space. Numerical results for eigenvalues evolution of obtained functional matrixes and for multifractal investigation are represented.
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Victor F. Dailyudenko, Victor F. Dailyudenko, "Fractal and multidimensional analysis of data from delay complex systems", Proc. SPIE 4384, Data Mining and Knowledge Discovery: Theory, Tools, and Technology III, (27 March 2001); doi: 10.1117/12.421080; https://doi.org/10.1117/12.421080

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