Interaction of the folded Whitney umbrella and swallowtail in slow–fast systems

The graph of a first integral of a smooth slow-fast system with two slow variables is a singular surface in the three-dimensional space; the variation of an external parameter on which the system depends gives rise to perestroikas ($=$transitions) of this surface. We find a normal form and present figures of the perestroika that describes the interaction between the swallowtail and folded Whitney umbrella on the graph of a first integral of a generic one-parameter family of such systems.