Potential V(x) and fixed points
Bifurcation diagram: x* vs r
Phase portrait ẋ = f(x,r) — flow arrows show dynamics
ẋ = rx − x³
V = −rx²/2 + x⁴/4
Supercritical pitchfork
V = −rx²/2 + x⁴/4
Supercritical pitchfork
Supercritical: stable branches x*=±√r appear for r>0 (soft bifurcation). Subcritical: unstable branches x*=±√(-r) collapse inward — hysteresis possible.