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Discrete Dynamics in Nature and Society
Volume 1 (1997), Issue 2, Pages 85-98

Sociodynamics applied to the evolution of urban and regional structures

Institute of Theoretical Physics, University of Stuttgart, Pfaffenwaldring 57/111, Stuttgart D-70550, Germany

Received 9 October 1996

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The article consists of two parts. In the first section the concepts of sociodynamics are briefly explained. Sociodynamics is a general modelling strategy for the quantitative description of dynamic processes in the human society. The central concepts of sociodynamics include transition rates depending on dynamic utilities and the master equation for the probability distribution over macrovariables. From it the set of nonlinear coupled differential equations for the quasi-meanvalues of the macrovariables can be derived.

In the second part this modelling strategy is applied to two “windows of perception” of the evolution of settlement structures: one model refers to the relatively fast urban evolution on the microscale and the other refers to the relatively slow regional evolution on the macroscale.

The micromodel considers the urban structure as a system of sites on which different kinds of buildings (dwellings, schools, stores, service-stations, factories...) can be erected. The step by step evolution of the city configuration is treated as a stochastic process guided by utility considerations. The sociodynamic formalization of this concept leads to equations for the evolution of the urban city configuration. Numerical simulations illustrate this urban “microdynamics”.

The macromodel treats the settlement formation in a region on a more global scale. The evolution of the density of economically active populations who produce and consume goods is considered. The driving force of density changes is the spatial difference of incomes motivating the individuals to migrate to locations of optimal income. This nonlinear process leads to the self-organisation of spatially heterogeneous population distributions forming the settlements. Their micro-structure can thereupon be treated by the micromodel.