05: Chaos and Catastrophies – Modeling the Unexpected

The main difference between chaos theory and catastrophe theory is that chaos can occur within a single dynamical system, whereas catastrophes occur in a parametrised family of systems. A catastrophe will occur if the parameters are gradually changed so that an equilibrium loses is stability causing the system to suddenly jump into another equilibrium. Hence catastrophe theory is particularly applicable to phenomena in which continuous causes give rise to discontinuous effects. In 1970 Thom classified the geometric shapes involved, which he called elementary catastrophes.
The Seminar will study some of these, and some applications in the physical, biological and behavioural science, including elasticity, buckling and light caustics; evolution in biology, hyperthyroidism in medicine; devaluation & inflation in economics, fear rage, and switches of mood perception in psychology, conflict and compromise in sociology, and works of Ibsen Jane Austin in literature.