0
$\begingroup$

I have a mapping function (cubic logistic map) f(x)=rx(1-x^2) and I need to make multiple bifurcation diagrams, showing stable equilibria and periodic orbits for 400 equally spaced r values between 0 and 3. Once for x_0=0.7 and another diagram for x_0=-0.7 Any help would be greatly appreciated!

$\endgroup$
1
  • 2
    $\begingroup$ Post what you've done so far... this is not a code-for-me-please community... $\endgroup$ – ciao Jun 1 '15 at 6:03
6
$\begingroup$

As ciao (rasher) has commented you are unlikely to receive assistance without showing your own attempt with Mathematica. Further, trying yourself is the best way to learn. This is an excellent resource to facilitate learning but is not substitution for your own efforts.

The following (which I sadly could not resist) is not a bifurcation diagram but perhaps will motivate your own attempts.

f[r_] := r # (1 - #^2) &;
func[r_, n_, x0_] := 
 Partition[Flatten[NestList[f[r] /@ # &, {x0, f[r][x0]}, n]], 2, 1]
Manipulate[
 Column[{Show[
    Plot[{f[r][x], x}, {x, 0, 1}, 
     Epilog -> {Red, PointSize[0.04], Point[{s, f[r][s]}]}], 
    Graphics[Arrow@func[r, n, s]]],
   ListPlot[NestList[f[r], s, n], Joined -> True, 
    PlotMarkers -> {Style[\[FilledDiamond], Red], 16}]}],
 {r, 0.1, 3, Appearance -> "Labeled"}, {s, 0.1, 1, 
  Appearance -> "Labeled"}, {n, Range[2, 20]}]

enter image description here

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.