(* Define the bifurcation function.
In this example, the following logistic function is used: f(mu,x) = mu*x*(1-x).
The starting value is x0.
Mu ranges between mumin and mumax.
The stepsize in my is del.
*)
bifurcation[
x0_,mumin_,mumax_,del_,nmax_,opts___Rule] := (
ListPlot[
Flatten[
Table[
Thread[
List[
mu,
Drop[
NestList[(mu # (1 - #))&, x0, nmax],
200
]
]
],
{mu,mumin,mumax,del}
],
1
],
opts
]
)

(* Create a bifurcation diagram. *)
bifurcation[
0.2,2.9,4.0,0.01,500,
AxesOrigin -> {2.8, 0},
PlotRange -> {{2.8,4},{0,1}},
AxesLabel -> {α, (Subscript[x, n])}
]