Fast and Slow Equations: The Development Patterns of Urban Settings

Abstract

The qualitative dynamics of city size is considered, and for this purpose the topics of slow and fast variables, equations, and equilibria are introduced, all within the framework of the theory of structural stability. The nature of urban development is discussed in general terms, and two specific models of city-size behavior are examined. In both models the key variables are the social costs associated with development and the degree of comparative advantage. The dynamic behavior of each type is derived, and an interpretation of their qualitative features is suggested. Finally, further extensions of this work and new directions for research are indicated.