Introduction and Applications of Stochastic Catastrophe Theory

Synopsis

Catastrophe Theory (CT) is a topological theory that provides a framework to analyze deterministic systems whose state variables respond discontinuously to smooth continuous changes in control variables. As a branch of bifurcation theory, CT deals directly with discontinuities without reference to any specific underlying mechanism. Since its conception by Rene Thom in the 1960s, CT has been applied to caustics, nonlinear oscillators, stability of black holes, and has acted as a stepping stone to singularity theory. Recent progress has been made in extending CT to stochastic systems. In this talk I will briefly introduce deterministic CT then focus on the development of Stochastic Catastrophe Theory (SCT). I will conclude with the application of SCT to X-ray flux data from the Cygnus X-1 galactic black hole.