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Function File: output = lyap_r (X)
Function File: output = lyap_r (X, paramName, paramValue, …)

Estimates the largest Lyapunov exponent of a given scalar data set using the algorithm described by Resentein et al. on the TISEAN refernce page:

http://www.mpipks-dresden.mpg.de/~tisean/Tisean_3.0.1/docs/chaospaper/citation.html

Input

X

Must be realvector. The output will be alligned with the input.

Parameters

m

Embedding dimension to use [default = 2].

d

Delay used [default = 1].

t

Window around the reference point which should be omitted [default = 0].

r

Minimum length scale for the neighborhood search [default = 1e-3].

s

Number of iterations in time [default = 10].

Switch

verbose

Gives information about the current epsilon while performing computation.

Output

Alligned with input. If input was a column vector than output contains two columns. The first contains the iteration number and the second contains the logarithm of the stretching factor for that iteration.

See also: demo lyap_r, lyap_k, lyap_spec.

Algorithms

The algorithms for this functions have been taken from the TISEAN package.

Demonstration 1

The following code

 idx = (1:2500).';
 in = sin (idx ./ 360) + cos (idx ./ 180);
 mmax = 15;

 cla reset
 hold on
 for i=2:mmax
   res = lyap_r (in, 'm', i, 'd', 6, 's',400,'t',200);
   plot (res(:,1),res(:,2),'r');
 endfor
 axis tight
 xlabel ("t [flow samples]");
 ylabel ("S(eps, embed, t)");
 hold off

Produces the following figure

Figure 1

Package: tisean