  Perturbing the external control parameters of nonlinear systems leads to
dramatic changes of its bifurcations. A branch of singular theory, the
catastrophe theory, analyses the generating function that depends on state and
control parameters. It predicts the formation of bifurcations as geometrically
stable structures and categorizes them hierarchically. We evaluate the
catastrophe diffraction integral with respect to two-dimensional cross-sections
through the control parameter space and thus transfer these bifurcations to
optics, where they manifest as caustics in transverse light fields. For all
optical catastrophes that depend on a single state parameter, we analytically
derive a universal expression for the propagation of all corresponding caustic
beams. We reveal that the dynamics of the resulting caustics can be expressed
by higher-order optical catastrophes. We show analytically and experimentally
that particular swallowtail beams dynamically transform to higher-order
butterfly caustics, whereas other swallowtail beams decay to lower-order cusp
catastrophes.
