Pitchfork Bifurcation

thingiverse

This object includes the pitchfork bifurcation plot and three corresponding potential energy curves. The bifurcation plot represents locations of equilibrium points of h/10+rx-x^3=dx/dt for different values of h, r, and x. Potential energy plots show potential energy of same system for three values of h, which causes system to lose its symmetry. Minimums and maximums of potential energy represent stable and unstable equilibrium points respectively. Objects were created in Mathematica with 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, Automatic, {-3.5, 2}}, PlotTheme -> "ThickSurface"] - Export["/Users/.../Vtab.stl", %, "STL"]