Liapunov Characteristic Number Diagram for Logistic map

Mapping-Configuration

Clear["Global`*"]
f[x_,r_]= r x (1-x)
fd[x_,r_]=D[f[x,r],x]
rmin=2.8; rmax=4; dr=0.01;
Nmax=1000;
x0=0.1;

LCN for each r  <two-loop Iterative Procedure>

LCNdata={};
r=rmin;
While[r<rmax,
{
lsum=0;
For[i=1,i<=Nmax, i++, 
{
lsum=lsum+Log[Abs[fd[x0,r]]];
x0=f[x0,r];
}];
lcn=lsum/Nmax;
AppendTo[LCNdata,{r,lcn}];
r=r+dr;
}]
Short[LCNdata,5]
ListPlot[LCNdata,Joined->True,AxesLabel->{"r","λ"}]