ABSTRACT
Phenomena involving sudden large variations traditionally have been assumed to be outside the reach of mathematical treatment, because they lacked what was considered to be an essential precondition, the continuity of the dependence relations between the variables. Recently, a branch of mathematics called catastrophe theory, one of the creations of the French mathematician René Thom (1972), has been applied to such discontinuous phenomena in biology (Thom 1969; 1971a; 1973a; Zeeman 1972a; 1974a) and physics (Fowler 1972; Shulman and Revzon 1972; Thom 1971b; 1973a; Zeeman 1972b; 1973; 1974c). The authors of the present article hope that their modest examples may suggest to specialists in the social sciences the possibility of applying catastrophe theory to similar discontinuous phenomena in their fields. (See also Harrison and Zeeman; Thom 1970; 1973b; Zeeman 1971; 1973; 1974c; 1974d; 1975.) The objective, in each of our examples, is the qualitative characterization of those points where small variations in some variable may cause large variations in a dependent variable, in other words those points where ‘catastrophic change’ may occur. This is the reason for the name catastrophe theory.
