V(x) = x⁴/4 − ax²/2 − bx
V'(x) = x³ − ax − b = 0

The fold surface (upper panel) shows equilibria as a function of (a,b).

Above the cusp (a>0): 3 roots possible — 2 stable, 1 unstable. System jumps discontinuously at fold edge.

Zeeman machine: physical catastrophe machine with spring and elastic band. Models opinion change, hysteresis, dogmatism.