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...
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03784371_v391_n8_p2564_DeMicco |
| Aporte de: |
| id |
todo:paper_03784371_v391_n8_p2564_DeMicco |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_03784371_v391_n8_p2564_DeMicco2023-10-03T15:33:00Z Sampling period, statistical complexity, and chaotic attractors De Micco, L. Fernández, J.G. Larrondo, H.A. Plastino, A. Rosso, O.A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 De Micco, L. Fernández, J.G. Larrondo, H.A. Plastino, A. Rosso, O.A. 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. |
| format |
JOUR |
| author |
De Micco, L. Fernández, J.G. Larrondo, H.A. Plastino, A. Rosso, O.A. |
| author_facet |
De Micco, L. Fernández, J.G. Larrondo, H.A. Plastino, A. Rosso, O.A. |
| author_sort |
De Micco, L. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_03784371_v391_n8_p2564_DeMicco |
| work_keys_str_mv |
AT demiccol samplingperiodstatisticalcomplexityandchaoticattractors AT fernandezjg samplingperiodstatisticalcomplexityandchaoticattractors AT larrondoha samplingperiodstatisticalcomplexityandchaoticattractors AT plastinoa samplingperiodstatisticalcomplexityandchaoticattractors AT rossooa samplingperiodstatisticalcomplexityandchaoticattractors |
| _version_ |
1807321228834242560 |