Some basic elements of catastrophe theory are discussed insofar as they relate to discontinuities observed in the allocation of economic activities in urban settings. The case of a dynamic model of the allocation of manufacturing and residential activities is presented in an open urban area as a model of a hyperbolic umbilic catastrophe. The dynamic equilibrium allocations of these two activities are identified as possible paths in the bifurcation set of the three parameter (control variables) and two behavioral-variables catastrophe type. A regulating function governing the urban system at the macroscale is discussed.