  The scaling of the time delay near a "bottleneck" of a generic saddle-node
bifurcation is well-known to be given by an inverse square-root law. We extend
the analysis to several non-generic cases for smooth vector fields. We proceed
to investigate $C^0$ vector fields. Our main result is a new phenomenon in
two-parameter families having a saddle-node bifurcation upon changing the first
parameter. We find distinct scalings for different values of the second
parameter ranging from power laws with exponents in (0,1) to scalings given by
O(1). We illustrate this rapid quantitative change of the scaling law by a an
overdamped pendulum with varying length.
