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I need to produce orbit diagrams for different values of x for the following equation:

f[r_][x_]:= r*x - x^3

I'm fairly new to Mathematica, so I haven't had a lot of practice using it. Basically I need to produce bifurcation diagrams for different values of x; then, using these plots, identify r values at which bifurcation occurs and determine the convergence ratio.

Any help would be much appreciated.

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A bit of help with the first stage...

f[r_,x_]:=r x-x^3;

To generate a bifurcation diagram...

ListPlot[
  Module[{x=0.5, n=1000},Apply[Join,Table[Thread[{r,NestList[f[r,#]&,x,n][[n/2;;-1]]}],{r,0,3,0.0125}]]], 
  Frame->True,Axes->False, ImageSize->600, PlotStyle->PointSize[Tiny]]

If you start reading up on the various functions used here you should be on your way at least.

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