Sampling period, statistical complexity, and chaotic attractors

We analyze the statistical complexity measure vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period τ and show that, if the Bandt and Pompe procedure is used to assign a probability distribution function (PDF) to the pertinent time series, the statistica...

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Detalles Bibliográficos
Publicado:	2012
Materias:	Chaos Nyquist reconstruction Sampling Takens reconstruction Chaotic attractors Correlation dimensions Delay Time Nyquist Reconstruction process Sampling period Statistical complexity Chaos theory Chaotic systems Probability distributions Time series
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v391_n8_p2564_DeMicco http://hdl.handle.net/20.500.12110/paper_03784371_v391_n8_p2564_DeMicco
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_03784371_v391_n8_p2564_DeMicco
record_format	dspace
spelling	paper:paper_03784371_v391_n8_p2564_DeMicco2023-06-08T15:40:16Z Sampling period, statistical complexity, and chaotic attractors Chaos Nyquist reconstruction Sampling Takens reconstruction Chaotic attractors Correlation dimensions Delay Time Nyquist Reconstruction process Sampling period Statistical complexity Chaos theory Chaotic systems Probability distributions Time series Sampling We analyze the statistical complexity measure vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period τ and show that, if the Bandt and Pompe procedure is used to assign a probability distribution function (PDF) to the pertinent time series, the statistical complexity measure (SCM) attains a definite maximum for a specific sampling period tM. On the contrary, the usual histogram approach for assigning PDFs to a time series leads to essentially constant SCM values for any sampling period τ. The significance of tM is further investigated by comparing it with typical times found in the literature for the two main reconstruction processes: the Takens' one in a delay-time embedding, on one hand, and the exact NyquistShannon reconstruction, on the other one. It is shown that tM is compatible with those times recommended as adequate delay ones in Takens' reconstruction. The reported results correspond to three representative chaotic systems having correlation dimension 2< D2<3. One recent experiment confirms the analysis presented here. © 2011 Elsevier B.V. All rights reserved. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v391_n8_p2564_DeMicco http://hdl.handle.net/20.500.12110/paper_03784371_v391_n8_p2564_DeMicco
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Chaos Nyquist reconstruction Sampling Takens reconstruction Chaotic attractors Correlation dimensions Delay Time Nyquist Reconstruction process Sampling period Statistical complexity Chaos theory Chaotic systems Probability distributions Time series Sampling
spellingShingle	Chaos Nyquist reconstruction Sampling Takens reconstruction Chaotic attractors Correlation dimensions Delay Time Nyquist Reconstruction process Sampling period Statistical complexity Chaos theory Chaotic systems Probability distributions Time series Sampling Sampling period, statistical complexity, and chaotic attractors
topic_facet	Chaos Nyquist reconstruction Sampling Takens reconstruction Chaotic attractors Correlation dimensions Delay Time Nyquist Reconstruction process Sampling period Statistical complexity Chaos theory Chaotic systems Probability distributions Time series Sampling
description	We analyze the statistical complexity measure vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period τ and show that, if the Bandt and Pompe procedure is used to assign a probability distribution function (PDF) to the pertinent time series, the statistical complexity measure (SCM) attains a definite maximum for a specific sampling period tM. On the contrary, the usual histogram approach for assigning PDFs to a time series leads to essentially constant SCM values for any sampling period τ. The significance of tM is further investigated by comparing it with typical times found in the literature for the two main reconstruction processes: the Takens' one in a delay-time embedding, on one hand, and the exact NyquistShannon reconstruction, on the other one. It is shown that tM is compatible with those times recommended as adequate delay ones in Takens' reconstruction. The reported results correspond to three representative chaotic systems having correlation dimension 2< D2<3. One recent experiment confirms the analysis presented here. © 2011 Elsevier B.V. All rights reserved.
title	Sampling period, statistical complexity, and chaotic attractors
title_short	Sampling period, statistical complexity, and chaotic attractors
title_full	Sampling period, statistical complexity, and chaotic attractors
title_fullStr	Sampling period, statistical complexity, and chaotic attractors
title_full_unstemmed	Sampling period, statistical complexity, and chaotic attractors
title_sort	sampling period, statistical complexity, and chaotic attractors
publishDate	2012
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03784371_v391_n8_p2564_DeMicco http://hdl.handle.net/20.500.12110/paper_03784371_v391_n8_p2564_DeMicco
_version_	1768544137042198528

Sampling period, statistical complexity, and chaotic attractors

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