Originally Posted by

**qtpipi** and then construct a bifurcation diagram.

Any help?

Hey, you into programming? Mathematica is a big help with this stuff. No I don't work for them; just know a good thing when I see it. You know what a bifurcation diagram is right? It illustrates the dependence of the critical points on the parameter. So just calculate the zeros of the right side as a function of h and then just plot the results. If you're interested, try interpreting the code below. It first finds the roots, selects only the real ones, then arranges them in a suitable order to connect the points and draw a smooth plot. Now, modify my code to construct the pitch-fork bifurcation for the second one.

Also, in the news yesterday was an article about tipping points in global warming:

Is There a Climate-Change Tipping Point? - TIME

Here's something fun: Explain what that has to do with this thread.

Code:

Clear[h]
myList =
Table[myRoots = x /. Solve[1/10 x (10 - x) - h == 0, x];
{h, #} & /@ myRoots,
{h, -5, 5, 0.1}];
myRealRoots =
Flatten[Select[myList, Element[#[[2]], Reals] &], 1];
curve = FindCurvePath[myRealRoots]
ListLinePlot[myRealRoots[[curve[[1]]]]]