The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Determination of the noise level of chaotic time series
Abstract
We propose a method to determine the amount of measurement noise present in a chaotic time series. If the data are embedded in a space of higher dimension than that strictly required to reconstruct the dynamics, the extra dimensions are dominated by the noise, which results in a certain shape of the correlation integral. For the case in which only Gaussian noise is present, this shape can be calculated analytically as a function of the noise level. Thus the noise level can be obtained from a simple function fit. The analytical result also shows that a noise level of more than 2% will obscure any possible scaling of the correlation integral and thus makes it impossible to estimate the correlation dimension.
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Cites
Characterization of Strange Attractors
Grassberger, P., & Procaccia, I. (1983) · Physical Review Letters · doi:10.1103/physrevlett.50.346 · Cited by 4,857
Extracting qualitative dynamics from experimental data
Broomhead, D. S., & King, G. P. (1986) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(86)90031-x · Cited by 2,278
Sauer, T., Yorke, J. A., & Casdagli, M. (1991) · Journal of Statistical Physics · doi:10.1007/bf01053745 · Cited by 2,045
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The dimension of chaotic attractors
Farmer, J. D., Ott, E., & Yorke, J. A. (1983) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(83)90125-2 · Cited by 1,104
NONLINEAR TIME SEQUENCE ANALYSIS
GRASSBERGER, P., SCHREIBER, T., & SCHAFFRATH, C. (1991) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127491000403 · Cited by 526
Self-citationSingular-value decomposition and the Grassberger-Procaccia algorithm
Albano, A. M., Muench, J., Schwartz, C., Mees, A. I., & Rapp, P. E. (1988) · Physical Review A · doi:10.1103/physreva.38.3017 · Cited by 460
Finite sample corrections to entropy and dimension estimates
Grassberger, P. (1988) · Physics Letters A · doi:10.1016/0375-9601(88)90193-4 · Cited by 287
A noise reduction method for signals from nonlinear systems
SAUER, T. D. (1992) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(92)90108-y · Cited by 153
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El-Barbary, A. A., Telling, R. H., Ewels, C. P., Heggie, M. I., & Briddon, P. R. (2003) · Physical Review B · doi:10.1103/physrevb.68.144107 · Cited by 579
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Metadata
- Authors
- Schreiber, T.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 1993-07-01
- Volume
- 48
- Issue
- 1
- Pages
- R13-R16
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W2065566139
- Cited by
- 311
- References
- 9
- FWCI
- 16.36
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
