Many mathematical models of real life problems are described by real zeros of smooth maps. The local zero structure of a singular smooth map may qualitatively change when the map is subjected to small perturbations. The changes include births and/or deaths of zeros. These materialize as the occurrence of a new solution type to the singular real life problem. Hence, the inevitable imperfections are the actual factors to determine the real world-solution type to occur. A qualitative change in the zero structures is called a bifurcation and the map is named a singularity.
