https://scholars.lib.ntu.edu.tw/handle/123456789/29919
標題: | 時間序列在資料重建之下嵌入相空間 Data Reconstruction of Time Series in Embedding Phase Space |
作者: | 何志偉 Ho, Chih-Wei |
關鍵字: | 時間序列;相空間與相空間曲線;奇異吸引子;延遲重構;嵌入空間;classical and relaxed Cantor set;Belousov-Zhabotinskii reaction;核磁共振;心律不整;Grassberger and Procaccia (D2 dimension);time series;phase space and curve;strange attractor;delay reconstruction;embedding space;NMR;Arrhythmia | 公開日期: | 2006 | 摘要: | When studying a physical phenomenon experimentally following the evolution of time, we measured and collected relevant one dimensional data and considered it correct even when the data appeared chaotic, we assumed the phenomenon is controlled by a strange attractor in an unknown phase space. This point of view induces the delay reconstruction method and embedding theorems due to Whitney, Takems, Sauer, Yorke, Casdagli. What follows then is to estimate the dimension of that strange attractor by Grassberger and Procaccia (D2 dimension) method in that embedded space with the dimension, or higher. Before doing so I tried the idea of making a description of the classical Cantor set which is defined only through logic and is an uncountable set while any time series is at most countable. Then I tried the same method to any relaxed Cantor set and “calculate” the dimension and demonstrate that time series description is applicable. Furthermore, from two sets of experimental data (1. Nuclear Magnetic Resonance (NMR) 2.Arrhythmias), they and we use the same algorithm to estimate the “fractal” dimension of the attractor of the dynamical system. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/59469 | 其他識別: | en-US |
顯示於: | 數學系 |
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ntu-95-R92221021-1.pdf | 23.53 kB | Adobe PDF | 檢視/開啟 |
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