Abstract :
In this paper, a sequel to Stewart [37], [38] we describe some of the recent applications of nonelementary catastrophe theory, especially the Golubitsky-Schaeffer approach to imperfect bifurcation. It is in these applications that the importance of Catastrophe Theory for the "hard" sciences becomes clearest, in that several of the applications make decisive contributions to problems that have been open for some time-even several decades. These include the phenomenon of mode-jumping in the buckling plate, the Benard Problem, and the effects of finite cylinders in the Taylor vortex problem. Other applications discussed include chemical reactions, nerve impulse transmission, and reaction-diffusion equations. "Nonelementary" is used here in the sense of Stewart [37], [38] to refer to extensions of the theory of elementary catastrophes that are applicable to problems not of gradient type. According to an arguably more useful distinction made by Zeeman [44], many become "elementary" in his sense. For applications of the original elementary catastrophes see Poston and Stewart 1251, Stewart [34]-[36], and Zeeman [43].
