Evaluating Lyapunov Exponent Spectra with Neural Networks
A. Maus and J.
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
Ref: A. Maus and J. C. Sprott, Chaos, Solitons &
Fractals 51, 13-21 (2013)
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