# Changes

,  13:45, 9 June 2015
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 &#61; 2}} is sufficient, but for an Ikeda map it is better to use {{Codeline|m &#61; 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 &#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]]

[[File:tisean_false_neigh.png|400px|center]]
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=== Finding Unstable Periodic Orbits ===
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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}}.
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{{Code|Finding unstable periodic orbits|<syntaxhighlight lang="octave" style="font-size:13px">
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# Create maps
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hen      = henon (1000);
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hen_noisy = hen + std (hen) * 0.02 .* (-6 + sum (rand ([size(hen), 12]), 3));
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# Find orbits
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up        = upo(hen(:,1), 2, 'p',6,'v',0.1, 'n', 100);
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</syntaxhighlight>}}

=== Nonlinear Prediction ===

=== Nonlinear Prediction ===
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