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TISEAN package: Difference between revisions
→Tutorials: adding Finding unstable periodic orbits tutorial
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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 = 2}} is sufficient, but for an Ikeda map it is better to use {{Codeline|m = 3}}. | 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]] | [[File:tisean_false_neigh.png|400px|center]] | ||
=== Finding Unstable Periodic Orbits === | |||
Here I will demonstrate how to find unstable periodic orbits. This section is based on the TISEAN documentation chapter [http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/node19.html#SECTION00053000000000000000 Finding unstable periodic orbits]. We will start by finding these orbits using function {{Codeline|upo}}. | |||
{{Code|Finding unstable periodic orbits|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
# Create maps | |||
hen = henon (1000); | |||
hen_noisy = hen + std (hen) * 0.02 .* (-6 + sum (rand ([size(hen), 12]), 3)); | |||
# Find orbits | |||
up = upo(hen(:,1), 2, 'p',6,'v',0.1, 'n', 100); | |||
</syntaxhighlight>}} | |||
=== Nonlinear Prediction === | === Nonlinear Prediction === | ||