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Journal article
FILTERED NOISE CAN MIMIC LOW-DIMENSIONAL CHAOTIC ATTRACTORS
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, v 47(4), pp 2289-2297
01 Apr 1993
PMID: 9960256
Abstract
This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity Of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of D2 is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos.
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Details
- Title
- FILTERED NOISE CAN MIMIC LOW-DIMENSIONAL CHAOTIC ATTRACTORS
- Creators
- P E Rapp - Drexel UniversityA M Albano - Bryn Mawr CollegeT I Schmah - Bryn Mawr CollegeL A Farwell - Human Brain Research Laboratory, 12944C Travilah Road, Potomac, Maryland 20854
- Publication Details
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, v 47(4), pp 2289-2297
- Publisher
- AMERICAN PHYSICAL SOC
- Number of pages
- 9
- Resource Type
- Journal article
- Language
- English
- Web of Science ID
- WOS:A1993KZ50700018
- Scopus ID
- 2-s2.0-0000785387
- Other Identifier
- 991019330617404721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Physics, Fluids & Plasmas
- Physics, Mathematical