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1,439 bytes added ,  13:39, 6 July 2015
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[[File:lyap_k.png|400px|center]]
 
=== Dimensions and entropies ===
This function uses a method to determine the minimum sufficient embedding dimension. It is based on the [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/node9.html#SECTION00032200000000000000 False Nearest Neighbors] section of the TISEAN documentation. As a demonstration we will create a plot that contains an Ikeda Map, a Henon Map and a Henon Map corrupted by 10% of Gaussian noise.
{{Code|Analyzing false nearest neighbors|<syntaxhighlight lang="octave" style="font-size:13px">
# Create maps
ikd = ikeda (10000);
hen = henon (10000);
hen_noisy = hen + std (hen) * 0.02 .* (-6 + sum (rand ([size(hen), 12]), 3));
# Create and plot false nearest neighbors
[dim_ikd, frac_ikd] = false_nearest (ikd(:,1));
[dim_hen, frac_hen] = false_nearest (hen(:,1));
[dim_hen_noisy, frac_hen_noisy] = false_nearest (hen_noisy(:,1));
plot (dim_ikd, frac_ikd, '-b*;Ikeda;',...
dim_hen, frac_hen, '-r+;Henon;',...
dim_hen_noisy, frac_hen_noisy, '-gx;Henon Noisy;');
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The {{Codeline|dim_*}} variables hold the dimension (so here 1:5), and {{Codeline|frac_*}} contain the fraction of false nearest neighbors. From this chart we can obtain the sufficient embedding dimension for each system. For a Henon Map {{Codeline|m &#61; 2}} is sufficient, but for an Ikeda map it is better to use {{Codeline|m &#61; 3}}.
[[File:tisean_false_neigh.png|400px|center]]
 
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