Catastrophe time scales and conventions

Abstract

The delay convention and the Maxwell convention, widely adopted in catastrophe theory, may be regarded as two extreme cases in a broad range of possibilities. A Fokker-Planck equation is introduced to interpolate between these two extremes. The two time scales associated with the Fokker-Planck equation are related to the critical curvature and the potential-barrier height. The canonical relaxation and diffusion time scale curves of the cusp catastrophe are presented. Quantitative conditions for the validity of one of these two conventions are given in terms of the time rate of change of the control parameters, the curvature at locally stable critical points, and a signal-to-noise ratio.