Urban evolution : studies in the mathematical ecology of cities

The main point of this book is that, while the underlying processes in urban dynamics may be very complicated, the macroscopic state of the urban system is simple, easily described and understood. Urban settings are shown to have internal clocks manifested by regular cycles developed within particular environments. A set of non-linear dynamic models based on the Volterra-Lotka formalism, appropriately adapted, are shown to account for certain basic qualitative features of urban systems. This formalism is particularly useful for analysing aspects of dynamic stability. Although the methodology of mathematical ecology is selec tively used in this book, no substantive equivalences with general ecology are made. Using empirical evidence, the book develops the thesis of a dynamic interconnectance among the components of the urban dynamic structure, so that non-linearities, multiplicity of equi libria, and bifurcations in urban dynamics are highlighted.

A major theme in the book is that model complexity often implies dynamical instability, a result known in mathematical ecology through the work of Robert May. This complexity vs. stability issue is central in modelling and understanding urban evolution. Recorded inter-urban growth patterns, extensively discussed in this book, exhibit stability which is attributed to highly selective interconnectance among inter acting cities. Whereas, the cause for observed intra-urban instability must be found in an extensive random interdependence among various land uses and zones within cities. Both, inter-urban stability and intra urban instability are demonstrated in a relative growth framework. A number of insights can be drawn from such an approach, and they are extensively analysed in the book.