Singularities, Bifurcations, and Catastrophe Theories

The first information on catastrophe theory appeared in the western press about ten years ago. In journals like “News Week” there were reports of a revolution in mathematics comparable with Newton’s invention of the differential and integral calculus. It was claimed that the new science, catastrophe theory, is much more valuable to mankind than mathematical analysis. While Newtonian theory only considers smooth, continuous processes, catastrophe theory provides a universal method for the study of all jump transitions, discontinuities, and sudden qualitative changes. There appeared hundreds of scientific and popular science publications in which catastrophe theory was applied to such diverse fields as, for instance, the study of heart beat, geometrical and physical optics, embryology, linguistics, experimental psychology, economics, hydrodynamics, geology, and the theory of elementary particles. Among the published works on catastrophe theory are studies of stability of ships, models for the activity of the brain and mental disorders, for rioting prisoners and for investors on the stock exchange, studies of the effects of alcohol on drivers and of the censor’s attitude towards pornographic literature.