What happens if you add a small imperfection to a system that has a saddle-node bifurcation?

When a small imperfection is introduced to a system with a saddle-node bifurcation, it can prevent the bifurcation from occurring at the predicted critical point. This imperfection may lead to the emergence of new equilibria or modify the stability of existing ones, potentially resulting in a shift in the system's behavior. Instead of the typical two equilibria merging and disappearing, the system might exhibit different dynamics, such as the persistence of one or both equilibria or the emergence of bifurcations at altered parameters.