A practical method for calculating largest Lyapunov exponents from small data sets

Physica D: Nonlinear Phenomena

Volumn 65, Issue 1-2, 1993, Pages 117-134

  Rosenstein, Michael T ^a   Collins, James J ^a   De Luca, Carlo J ^a  

^a BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 43949166788     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(93)90009-P     Document Type: Article

References (41)

1. Prediction in chaotic nonlinear systems: methods for time series with broadband Fourier spectra
2. Calculating the dimension of attractors from small data sets
3. Singular-value decomposition and the Grassberger-Procaccia algorithm
4. Using higher-order correlations to define an embedding window
5. Kolmogorov entropy of a dynamical system with increasing number of degrees of freedom
6. Kolmogorov entropy and numerical experiments
7. An improved method for estimating Lyapunov exponents of chaotic time series
8. Extracting qualitative dynamics from experimental data
9. Computing the Lyapunov spectrum of a dynamical system from observed time series
10. Nonlinear prediction of chaotic time series
11. Empirical and theoretical evidence of economic chaos
12. Hierarchical training of neural networks and prediction of chaotic time series
13. Lyapunov exponents from time series
14. Fundamental limtations for estimating dimensions and Lyapunov exponents in dynamical systems
15. Ergodic theory of chaos and strange attractors
16. Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data
17. Predicting chaotic time series
18. Chaotic time series analysis of epileptic seizures
19. Independent coordinates for strange attractors from mutual information
20. Characterization of strange attractors
21. Estimation of the Kolmogorov entropy from a chaotic signal
22. A two-dimensional mapping with a strange attractor
23. Proper choice of the time delay for the analysis of chaotic time series
24. Deterministic Nonperiodic Flow
25. Oscillation and chaos in physiological control systems
26. A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems
27. Geometry from a time series
28. The statistical properties of dimension calculations using small data sets
29. Calculation of Lyapunov exponents through nonlinear adaptive filters
30. An equation for hyperchaos
31. An equation for continuous chaos
32. Measurement of the Lyapunov spectrum from a chaotic time series
33. Practical Methods of Measuring the Generalized Dimension and the Largest Lyapunov Exponent in High Dimensional Chaotic Systems
34. A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems
35. Calculation of Lyapunov exponents avoiding spurious elements
36. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
37. Detecting strange attractors in turbulence
38. Calculating the rate loss of information from chaotic time series by forecasting
39. Determining Lyapunov exponents from a time series
40. Method for calculating a Lyapunov exponent
41. Estimating the Lyapunov-exponent spectrum from short time series of low precision