Rank-size distribution of settlement systems: A stable attractor in urban growth

A further step towards a dynamic model for the observed size distribution of a system of settlements is presented. The occurrence and temporal stability of the rank-size distribution is obtained as the result of adynamic self-organizing process of the nested system of settlements. The inherent time scale;of this self-organizing process and the obtained hierarchical structure are related to the generally low inter-settlement mobility of urban population, the tendency of the population to agglomerate, distance effects and preference effects. The well-known migration model of Weidlich and Haag is used as starting point and three approaches to express the attractivity in the system are compared. The stationary state is investigated in detail under some Limiting conditions.