REVIEW ARTICLE: Catastrophe theory in physics

A discussion is presented of catastrophe theory, with attention to the developmental feedback between this field of mathematics and its applications in the physical sciences. Prominent concepts of catastrophe theory are co-dimension, determinacy, unfoldings, and organizing centers. The ways in which these concepts may be used are shown in light of specific applications taken from the literature, and the methods are generalized to areas not yet recognized to be within the purview of catastrophe theory. Note is taken of the philosophical background provided for this body of theory by the topological dynamics concept of structural stability. Catastrophe theory is in conclusion characterized as an important contribution to the understanding of nonlinear phenomena.