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TISEAN package: Difference between revisions
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</syntaxhighlight>}} | </syntaxhighlight>}} | ||
[[File:lyap_k.png|400px|center]] | [[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;'); | |||
</syntaxhighlight>}} | |||
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 = 2}} is sufficient, but for an Ikeda map it is better to use {{Codeline|m = 3}}. | |||
[[File:tisean_false_neigh.png|400px|center]] | |||