Determining Lyapunov exponents from a time series
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LE is a tool used to visualize the separation of trajectories from two initial values with minimal error over time.
“When two initial values with minimal error are applied to the same chaotic system, the trajectories they generate will be separated exponentially over time.LE is a tool used to visualize this phenomenon [21].”
From Chaos-Based Image Encryption: Review, Application, and Challenges (2023) · cites this paper as [21]
Cites
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“We should obtain an embedding if m is chosen to be greater than twice the dimension of the underlying attractor [34].”
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Rajendra Acharya, U., Paul Joseph, K., Kannathal, N., Lim, C. M., & Suri, J. S. (2006) · Medical & Biological Engineering & Computing · doi:10.1007/s11517-006-0119-0 · Cited by 2,820 · see citing works
COPASI—a COmplex PAthway SImulator
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Chaos-Based Image Encryption: Review, Application, and Challenges
Zhang, B., & Liu, L. (2023) · Mathematics · doi:10.3390/math11112585 · Cited by 328 · see citing works
“LE is a tool used to visualize this phenomenon [21].”
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A new hyperchaotic map and its application in an image encryption scheme
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- Authors
- Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A.
- Affiliations
- The University of Texas at Austin (US)
- ORCID
- Swinney, Harry L.
- Venue
- Physica D: Nonlinear Phenomena
- Publisher
- Elsevier BV
- Published
- 1985-07
- Volume
- 16
- Issue
- 3
- Pages
- 285-317
- ISSN
- 0167-2789 (ISSN-L)
- OpenAlex
- W2152254020
- Cited by
- 9,499
- References
- 1
- Citations by year
- 2026: 418 · 2025: 416 · 2024: 420 · 2023: 412 · 2022: 483 · 2021: 472 · 2020: 448 · 2019: 430 · 2018: 441 · 2017: 365 · 2016: 316 · 2015: 303 · 2014: 302 · 2013: 289 · 2012: 252
- FWCI
- 29.49
- Type
- journal article
- Language
- en
- Open access
- green
- hal.science
- Licence
- Locations
- Physica D Nonlinear Phenomena (publishedVersion)
- HAL (submittedVersion, other-oa)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Keywords
- Lyapunov exponents, time series analysis, chaos, nonlinear dynamics, data-driven estimation
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