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Evaluating Lyapunov exponent spectra with neural networks

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  • Maus, A.
  • Sprott, J.C.

Abstract

A method using discrete cross-correlation for identifying and removing spurious Lyapunov exponents when embedding experimental data in a dimension greater than the original system is introduced. The method uses a distribution of calculated exponent values produced by modeling a single time series many times or multiple instances of a time series. For this task, global models are shown to compare favorably to local models traditionally used for time series taken from the Hénon map and delayed Hénon map, especially when the time series are short or contaminated by noise. An additional merit of global modeling is its ability to estimate the dynamical and geometrical properties of the original system such as the attractor dimension, entropy, and lag space, although consideration must be taken for the time it takes to train the global models.

Suggested Citation

  • Maus, A. & Sprott, J.C., 2013. "Evaluating Lyapunov exponent spectra with neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 13-21.
  • Handle: RePEc:eee:chsofr:v:51:y:2013:i:c:p:13-21
    DOI: 10.1016/j.chaos.2013.03.001
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    References listed on IDEAS

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    1. Gencay Ramazan & Dechert W. Davis, 1996. "The Identification of Spurious Lyapunov Exponents in Jacobian Algorithms," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(3), pages 1-12, October.
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    Cited by:

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    2. Juan. J. Flores & José R. Cedeño González & Héctor Rodríguez & Mario Graff & Rodrigo Lopez-Farias & Felix Calderon, 2019. "Soft Computing Methods with Phase Space Reconstruction for Wind Speed Forecasting—A Performance Comparison," Energies, MDPI, vol. 12(18), pages 1-19, September.
    3. Anagnostidis, Panagiotis & Emmanouilides, Christos J., 2015. "Nonlinearity in high-frequency stock returns: Evidence from the Athens Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 473-487.

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