Evaluating Lyapunov Exponent Spectra with Neural Networks

A. Maus and J. C. Sprott
Physics Department, University of Wisconsin, 1150 University Ave., Madison, WI 53706, USA

Received 12 June 2012; Accepted 6 March 2013; Available online 9 April 2013


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 Henon map and delayed Henon 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.

Ref: A. Maus and J. C. Sprott, Chaos, Solitons & Fractals 51, 13-21 (2013)

The complete paper is available in PDF format.

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