ABSTRACT
In this chapter, we explore the progress of applications of catastrophe theory and bifurcation in a number of other disciplines and see if we can learn any more about possible analytical methods for urban systems. The most substantial progress has been in disciplines like physics, especially optics, and engineering (beams, stability of ships, and so on, switching problems in electrical and chemical engineering). However, these problems are unlike those we appear to face sin urban analysis (though a possible exception is the study of phase transitions in physics, which is still a controversial matter). There is least progress in the social sciences, where we might expect to look for analogies. It is not easy to see useful analogues from the applications so far in psychology or sociology (except possibly in being aware of the consequences of bimodality or trimodality in behavioural models: that is, suggesting an under lying cusp or butterfly manifold).
