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=== Lyapunov Exponents ===
 
=== Lyapunov Exponents ===
Here I will demonstrate how to use the function {{Codeline|lyap_k}}. It estimates the maximal Lyapunov exponent from 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 estimate the maximal Lyapunov exponent for various embedding dimensions and then plot them.  
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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);
# Estimate Lyapunov exponents
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# 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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