The fold catastrophe is exemplified by the critical point of the
function f(x) = x3. This critical point is
unstable: perturbing the function to f(x) = x3
+ ax gives a function with a maximum and a minimum near
zero if a is negative, no matter how small, and no
critical point at all if a is positive.
A typical one-dimensional section will follow the parameter a :
the energy minumum that exists for a < 0 disappears
as the section crosses a = 0 .
The corresponding verb class is
represented by "The day ends" if the section is traversed
from negative a to positive and "The day begins"
if it is traversed in the opposite direction.