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Independent coordinates for strange attractors from mutual information. (English) Zbl 1184.37027
Summary: The mutual information \(I\) is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction. An \(N \log N\) algorithm for calculating \(I\) is presented. As proposed by Shaw, a minimum in \(I\) is found to be a good criterion for the choice of time delay in phase-portrait reconstruction from time-series data. This criterion is shown to be far superior to choosing a zero of the autocorrelation function.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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