# 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.

## logmap.tgz

### Function

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

### Installation

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.