22 March 1999 Nonlinear time series processing by means of ideal topological stabilization analysis and scaling properties investigation
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Abstract
The conditions of topological stabilization for Takens attractor are investigated when enlarging phase space dimension by means of topological dependences analysis and asymptotical estimations calculation. It has been shown that ideal topological stabilization is equivalent to presence of linearized segmentation properties in time series under investigation, these properties being invariant concerning scale of partition. The exact ideal topological stabilization appears to be impossible for nonlinear time series, so we have to consider asymptotical estimations of convergence to exact stabilization. Some statistical characteristics of investigated attractor have been defined by relatively- difference investigation of obtained topological curves.
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Victor F. Dailyudenko, Victor F. Dailyudenko, } "Nonlinear time series processing by means of ideal topological stabilization analysis and scaling properties investigation", Proc. SPIE 3722, Applications and Science of Computational Intelligence II, (22 March 1999); doi: 10.1117/12.342916; https://doi.org/10.1117/12.342916
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