Reaction-diffusion Model Describing the Morphogenesis of Urban Systems in the US

Urbanization is currently one of the greatest challenges facing mankind. In order to be able to anticipate the rapid changes in urban structures, models are in need, mapping the morphological development of these structures. In this paper we present an urban development model that is based on reaction diffusion equations and can be interpreted sociologically. We apply this model to the urban development of US-American cities and show that this very simple model can already map basic characteristics of urban development.