Maximal Lyapunov exponent

lyapunov -d# -m# -M# -t# -r# [-s# -n# -k# -o outfile -l# -x# -c# -V# -h] file

-d delay
-m minimal embedding dimension
-M maximal embedding dimension
-t minimal time separation
-r diameter of initial neighbourhoods
-s time steps over which expansion is followed (100)
-n minimal number of reference points (all)
-k minimal number of neighbours for reference points (10)
-l number of values to be read (all)
-x number of values to be skipped (0)
-c column to be read (1 or file,#)
-o output file name, just -o means file_lyap
-V verbosity level (0 = only fatal errors)
-h show this message
Provides data for a scaling plot that can be used to determine the largest Lyapunov exponent of a scalar time series. The output file file_lyap contains the time seperation and the averaged phase space distance. Results for consecutive values of the embedding dimension are seperated by double blank lines.

This routine is based on

H. Kantz,
A robust method to estimate the maximal Lyapunov exponent of a time series,
Phys. Lett. A 185, 77 (1994).

See also lyap_r

Usage example

Try also just running: gnuplot lyapunov.gnu in the examples directory.

> henon -l10000 > data
> lyapunov -d1 -m2 -M3 -t50 -r0.005 -s20 data -o

gnuplot> set logscale y
gnuplot> set yrange [0.001:1]
gnuplot> plot 'data_lyap', exp(0.42*x)/400

lyapunov analysis

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