8. Criticality and Urban Retail Structure: Aspects of Catastrophe Theory and Bifurcation

There is now much experience of building models of the location of population and economic activities in cities and associated flows. It has proved more difficult to model the evolution of the underlying structure. A specific example will be used to illustrate both the achievements and the problems in this paper: we model the flows of cash from people at their residences to shopping centres and this enables us to predict the revenue attracted to particular locations. The structural problem is the study of the evolution and dynamics of the location and size of the shopping centres. It will be shown that there are surfaces of critical value (in parameter space) of locational parameters on one 'side' of which development at that location is possible and on the other side, not. It is suggested that such studies of criticality can form the basis of the theory of evolution of urban structures. -Author