  We study the pattern of activated trajectories in a double well system
without detailed balance, in the weak noise limit. The pattern may contain
cusps and other singular features, which are similar to the caustics of
geometrical optics. Their presence is reflected in the quasipotential of the
system, much as phase transitions are reflected in the free energy of a
thermodynamic system. By tuning system parameters, a cusp may be made to
coincide with the saddle point. Such an anomalous cusp is analogous to a
nonclassical critical point. We derive a scaling law, and nonpolynomial
`equations of state', that govern its bifurcation into conventional cusps.
