Catastrophe theory: a contribution to the study of urban systems?

Abstract

The possibility of applying Thorn's catastrophe theory to the study of urban systems is discussed in broad terms, the emphasis being laid on the importance it attaches to the idea of morphogenesis -- changes in structural form. The theory is introduced through the idea of a system being composed of a control manifold and a behaviour manifold which, together, form the system space; the system's possible behaviours lie in a behaviour subset of this space. Critical regions occur in the behaviour set where the kind of behaviour observed undergoes a catastrophic change of form. Control points associated with these changes form the catastrophe set for the system, and the control manifold is partitioned into various regions where the different behaviours are located. The system's behaviour is governed by families of regulating (potential) functions and supplementary conventions such as Maxwell's, the Perfect Delay, etc. There follows an extensive and illustrated description of twelve elementary catastrophes (including Thorn's 'magnificent seven'). The article concludes with a note of the few existing applications in urban studies and a brief summary of some technical details.