Physics – General Physics
Scientific paper
Oct 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983phrva..28.2591g&link_type=abstract
Physical Review A - General Physics, 3rd Series (ISSN 0556-2791), vol. 28, Oct. 1983, p. 2591-2593. Research supported by the Is
Physics
General Physics
347
Entropy, Kolmogoroff Theory, Random Signals, Strange Attractors, Time Signals, Chaos, Statistical Correlation, Time Series Analysis
Scientific paper
A method to estimate the Kolmogorov entropy K directly from a time signal is proposed which should prove valuable for characterizing experimental chaotic signals. A new quantity K(2) is defined which is zero or larger, equal to or less than K, infinite for random systems, and unequal to zero for chaotic systems. For typical systems K(2) turns out to be numerically close to K and thus has an advantage over the topological entropy h. While h greater than zero is a necessary but not sufficient condition for observable chaos, K(2) greater than zero is a sufficient condition for chaos. The most important property of K(2) is that it can be extracted fairly easily from an experimental signal. The proposed method is tested on a few examples, showing that a very good lower bound on the metric entropy of a strange attractor can be obtained from an experimental time series.
Grassberger Peter
Procaccia Itamar
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