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TISEAN package

1,084 bytes added, 15:12, 16 June 2015
→‎Tutorials: added 'Lyapunov Exponents'
Once both results are compared it is quite obvious that for this particular example {{Codeline|ghkss}} is superior to {{Codeline|lazy}}. The TISEAN documentation points out that this is not always the case.
[[File:tisean_nl_noisereduction_2.png|400px|center]]
 
=== Lyapunov Exponents ===
Here I will demonstrate how to use the function {{Codeline|lyap_k}}. It create Lyapunov Exponents for a time series (more information available [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">
# Create time series
in = sin((1:2500).'./360) + cos((1:2500).'./180);
# Create Lyapunov exponents
mmax_val = 20
lyap_exp = lyap_k (in, 'mmin',2,'mmax',mmax_val,'d',6,'s',400,'t',500);
</syntaxhighlight>}}
In this function the output ({{Codeline|lyap_exp}} is a {{Codeline|5 x 20}} struct array. We will only use one row for the plot.
{{Code|Plotting Lyapunov exponents|<syntaxhighlight lang="octave" style="font-size:13px">
cla reset
hold on
for j=2:mmax_val
plot (lyap_exp(1,j-1).exp(:,1),lyap_exp(1,j-1).exp(:,2),'r');
endfor
xlabel ("t [flow samples]");
ylabel ("S(eps, embed, t)");
hold off
</syntaxhighlight>}}
[[Category:Octave-Forge]]
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