Evaluating Lyapunov exponent spectra with neural networks

A method using discrete cross-correlation for identifying and removing spurious Lyapunov exponents when embedding experimen tal data in a dimension greater than the origina l system is introduce d. 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. 2013 Elsevier Ltd. All rights reserved.