Pitchfork Bifurcation

This object includes the pitchfork bifurcation plot and three corresponding potential energy curves. The bifurcation plot represents the locations of the equilibrium points of
h/10+rx-x^3=dx/dt
for different values of h, r, and x. The potential energy plot shows the potential energy of the same system for three values of h (which causes the system to lose its symmetry). The minimums and maximums of the potential energy represent the stable and unstable equilibrium points respectively.
The objects were created in Mathematica with the following lines of code:
- ContourPlot3D[
h/10 + r x - x^3 == 0, {h, -.5, .5}, {r, -1.5, 2}, {x, -2, 2}, MaxRecursion -> 15, PlotPoints -> 115, PlotTheme -> "ThickSurface"]
- Export["/Users/.../Bi1.stl", %, "STL"]
- Plot3D[Table[-(h*x/10 + r*x^2/2 - x^4/4), {h, {-5, 0, 5}}], {r, -.5, 3}, {x, -2.75, 2.75}, MaxRecursion -> 15, PlotPoints -> 115, AspectRatio -> 1, PlotRange -> {Automatic, Automa