Bursts and Avalanches: The Dynamics of Polycentric Urban Evolution

Urban construction activities are subject to periods of fast expansion followed by periods of slow growth. Some of these expansions are limited in size, while others are huge. Therefore, it is not surprising that equilibrium-oriented classical models of urban spatial structure are hard pressed to explain the formation of modern cities with polycentric structure and births of subcenters in particular. To understand the development of cities' spatial patterns we present a model of urban spatial dynamics that is driven by two types of real-estate entrepreneurs that differ in their degree of risk aversion. The developers act in the shadow of the city planning board that formulates urban development policy and defines the boundaries of future residential expansions. The model's salient feature is the time lag between the time of purchase of property rights by land developers and the time of the realization of revenues. We assume that this lag varies in space, being much larger in locations that are not zoned for building. It can be reduced by the planning board in cases of high demand for dwellings. We use the model to demonstrate how the interaction between demand for dwellings, the choices taken by each type of developer, and planning policies leads to the creation of new urban subcenters. The model dynamics are characterized by long out-of-equilibrium periods followed by sudden bursts of construction activity that resembles self-organized criticality.