Article ID Journal Published Year Pages File Type
1892824 Chaos, Solitons & Fractals 2013 9 Pages PDF
Abstract

•Cross-correlation is employed to remove spurious Lyapunov exponents from a spectrum.•Neural networks are shown to accurately model Lyapunov exponent spectra.•Neural networks compare favorably to local linear fits in modeling Lyapunov exponents.•Numerical experiments are performed with time series of varying length and noise.•Methods perform reasonably well on discrete time series.

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.

Related Topics
Physical Sciences and Engineering Physics and Astronomy Statistical and Nonlinear Physics
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