THE CHALLENGE OF MODELLING CATASTROPHE EVENTS The very last painting by Salvador Dali was titled The Swallow�s Tail � Series on Catastrophes. Dali was greatly interested in the catastrophe theory developed by the French mathematician Ren� Thom, and referred to it as �the most beautiful aesthetic theory in the world�. Thom�s catastrophe theory describes how small changes in parameters of a stable nonlinear system can lead to a loss of equilibrium and dramatic, on the level of catastrophic, change in the state of the system. Thom described equilibrium topological surfaces and corresponding discontinuities that exist under certain conditions. An equilibrium state is associated with the minimum of its potential function; according to the catastrophe theory, a phase transition or a discontinuity can be associated with only a limited number of stable geometric structures categorising degenerate critical points of the potential function. The Swallow�s Tail includes two of the so-called elemen...