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Measurement of the Lyapunov Spectrum from a Chaotic Time Series
Abstract
The exponential divergence or convergence of nearby trajectories (Lyapunov exponents) is conceptually the most basic indicator of deterministic chaos. We propose a new method to determine the spectrum of several Lyapunov exponents (including positive, zero, and even negative ones) from the observed time series of a single variable. We have applied the method to various known model systems and also to the Rayleigh-B\'enard experiment, and have elucidated the dependence of the Lyapunov exponents on the Rayleigh number.
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Cited by
Recurrent neural networks employing Lyapunov exponents for EEG signals classification
GULER, N., UBEYLI, E., & GULER, I. (2005) · Expert Systems with Applications · doi:10.1016/j.eswa.2005.04.011 · Cited by 503
Data based identification and prediction of nonlinear and complex dynamical systems
Wang, W.-X., Lai, Y.-C., & Grebogi, C. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.06.004 · Cited by 299
Pathological tremors: deterministic chaos or nonlinear stochastic oscillators?
Timmer, J., Häussler, S., Lauk, M., & Lücking, C.-H. (2000) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.166494 · Cited by 130
Metadata
- Authors
- Sano, M., & Sawada, Y.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1985-09-02
- Volume
- 55
- Issue
- 10
- Pages
- 1082-1085
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W1966617449
- Cited by
- 982
- References
- 0
- FWCI
- 9.49
- Type
- journal article
- Language
- en
- Open access
- closed
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- Sano, M., & Sawada, Y. (1985). Measurement of the Lyapunov Spectrum from a Chaotic Time Series. Physical Review Letters. https://doi.org/10.1103/physrevlett.55.1082
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