Bifurcation diagram of the logistic map.

I have written logmap for an collegue of mine. I wanted to show him that the numerical computation of the limit cycles can be speed-up and improved in quality by some kind of shooting method.



The program logmap computes the bifurcation diagram and the Lyapunov exponents of the logistic map x(n+1) = λ x(n) ( 1.0 + x(n) ) with the bifurcation parameter λ∈[0.5,4] . Below you can see the graphs of the computed data.


To install the package you need a linux box, a gcc compiler, and gnuplot.

Get the file logmap.tgz and extract it by
tar -xzvf logmap.tgz
The archive file logmap.tgz extracts into a directory Logmap relative to the current path. Change to that directory and call
make all
that should create the eps-files traj.eps and lyap.eps with the bifurcation diagram and the graph of the Lyapunov exponent versus λ. Both pictures are shown below.
   Missing file traj.png      Missing file lyap.png