Determining Lyapunov Exponents from a Time Series

Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985). Determining Lyapunov Exponents from a Time Series. Physica D, 2789(85), 285-317.

Type

Journal article

Intellectual base

Primary research

Year

1985

DOI

10.1016/0167-2789(85)90011-9

Link

https://chaos.utexas.edu/publications/Determining_Lyapunov_exponents_from_a_time_series

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Chaos
  • A meteorologist characterizing forecast limits, a cardiologist analyzing arrhythmia dynamics, and an ecologist modeling irregular population cycles are all doing the same structural work: identify the deterministic rule (approximately), test for sensitive dependence using time-series methods of the kind Wolf, Swift, Swinney, and Vastano (1985) introduced for estimating Lyapunov exponents from experimental data

    This sourceFirst general algorithms for estimating non-negative Lyapunov exponents from experimental scalar time series; demonstrated on the Belousov-Zhabotinsky reaction and Couette-Taylor flow.

Domain-specific

• Lyapunov Exponent
  • A positive exponent can arise along an unstable nonchaotic orbit or in an unbounded trajectory; finite-time estimates can be positive because of transients; and noise, nonstationarity, embedding error, or insufficient data can bias empirical estimates.

Verification

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