What have you done so far?
Your function L(e) is the logistic map function, with r=3.99. You have not specified the r-value for the logistic map function f(x)=r*x*(1-x), where 0<r<4. Therefore your system has two adjustabole parameters: r and e. Do you want to make a bifurcation diagram for r (at a fixed e) or for e (at a fixed r)?
You make the logistic map by simulating the system until it reaches a limit cycle, or until you give up, for many values of the parameter (r or e). Then you plot the parameter (r or e) on the x-axis, and the corresponding elements of the limit cycle as the corresponding y-values.
