1999
DOI: 10.1103/physrevlett.82.1144
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Construction of Symbolic Dynamics from Experimental Time Series

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Cited by 142 publications
(118 citation statements)
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“…Such applications include vision and recognition by Allili, Mischaikow and Tannenbaum [1], hybrid systems and control theory by Ames [2], rigorous verification of dynamics from experimental data by Mischaikow, Mrozek, Reiss and Szymczak [19], and global analysis of large data sets by the first author and Carlsson [5]. In the last example, there is a growing literature on the importance of persistent homologyhomology classes which persist as one changes a parameter in the system.…”
Section: Resultsmentioning
confidence: 99%
“…Such applications include vision and recognition by Allili, Mischaikow and Tannenbaum [1], hybrid systems and control theory by Ames [2], rigorous verification of dynamics from experimental data by Mischaikow, Mrozek, Reiss and Szymczak [19], and global analysis of large data sets by the first author and Carlsson [5]. In the last example, there is a growing literature on the importance of persistent homologyhomology classes which persist as one changes a parameter in the system.…”
Section: Resultsmentioning
confidence: 99%
“…Many procedures have been proposed for the election of P ∈ Ω. We can mention techniques based on symbolic dynamics [7], Fourier analysis [8], and wavelet transform [9] (among others). The applicability of these approaches depends on the data-characteristics, i.e., stationarity, length of the series, parameter-variations, levels of noise-contamination, etc.…”
Section: Introductionmentioning
confidence: 99%
“…We can mention, among others: (a) frequency count [35] (b) procedures based on amplitude statistics (histograms) [36], (c) binary symbolic dynamics [37], (d) Fourier analysis [38] and, (e) wavelet transform [39]. Their applicability depends on particular characteristics of the data such as stationarity, length of the time series, variation of the parameters, level of noise contamination, etc.…”
Section: Methodologies For Selecting Pdfsmentioning
confidence: 99%