The preliminary design of a differentiated compliance anchoring system (DICAS) is assessed based on stability of its slow-motion nonlinear dynamics using bifurcation theory. The system is to be installed in the Campos Basin, Brazil, for a fixed water depth under predominant current directions. Catastrophe sets are constructed in a two-dimensional parametric design space, separating regions of qualitatively different dynamics. Stability analyses define the morphogeneses occurring across bifurcation boundaries to find stable and limit cycle dynamical behavior. These tools allow the designer to select appropriate values for the mooring parameters without resorting to trial and error, or extensive nonlinear time simulations. The vessel equilibrium and orientation, which are functions of the environmental excitation and their motion stability, define the location of the top of the production riser. This enables the designer to verify that the allowable limits of riser offset are satisfied. The mathematical model consists of the nonlinear, horizontal plane fifth-order large-drift, low-speed maneuvering equations. Mooring lines are modeled by open-water catenary chains with touchdown effects and include nonlinear drag. External excitation consists of time-independent current, wind, and mean wave drift.