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== Porting TISEAN == | == Porting TISEAN == | ||
This section | This section will focus on demonstrating the capabilities of the TISEAN package. The previous information about the porting procedure has been moved [[TISEAN_package:Procedure|here]]. | ||
Current ideas and future plans are available on a board loacated [https://trello.com/b/hJS1Q8wN here] | |||
== Tutorials == | == Tutorials == | ||
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=== Lyapunov Exponents === | === Lyapunov Exponents === | ||
Here I will demonstrate how to use the function {{Codeline|lyap_k}}. It | Here I will demonstrate how to use the function {{Codeline|lyap_k}}. It creates Lyapunov Exponents for a time series (more information available from the TISEAN documentation located [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/node27.html here]). In this tutorial we will create a Lyapunov Exponent for various embedding dimensions and then plot them. | ||
{{Code|Creating Lyapunov exponents|<syntaxhighlight lang="octave" style="font-size:13px"> | {{Code|Creating Lyapunov exponents|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
# Create time series | # Create time series | ||
in = sin((1:2500).'./360) + cos((1:2500).'./180); | in = sin((1:2500).'./360) + cos((1:2500).'./180); | ||
# | # Create Lyapunov exponents | ||
mmax_val = 20 | mmax_val = 20 | ||
lyap_exp = lyap_k (in, 'mmin',2,'mmax',mmax_val,'d',6,'s',400,'t',500); | lyap_exp = lyap_k (in, 'mmin',2,'mmax',mmax_val,'d',6,'s',400,'t',500); | ||
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[[File:lyap_k.png|400px|center]] | [[File:lyap_k.png|400px|center]] | ||
=== Dimensions and | === Dimensions and entropies === | ||
This | 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| | {{Code|Analyzing false nearest neighbors|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
# Create maps | # Create maps | ||
ikd = ikeda (10000); | |||
hen = henon (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>}} | </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}}. | |||
The | [[File:tisean_false_neigh.png|400px|center]] | ||
# | |||
[[File: | |||
[[ | [[Category:Octave-Forge]] | ||
== External links == | == External links == | ||
* [https://bitbucket.org/josiah425/tisean Bitbucket repository ] where the porting is taking place. | * [https://bitbucket.org/josiah425/tisean Bitbucket repository ] where the porting is taking place. | ||
* [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/ TISEAN package website] where the package is described along with references to literature, tutorials and manuals. | * [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/ TISEAN package website] where the package is described along with references to literature, tutorials and manuals. | ||