### 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

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