The nonlinear interactive dynamic process of settlement formation is a fundamental issue in spatial analysis. Our proposed model integrates the economic and migratory sectors as endogenous variables to describe the evolution of continuous population distributions as a self-organizing process. The model has been designed as follows: an ensemble of populations is described by the respective population densities over the plane, with the latter being tessellated into equivalent unit cells. Populations produce commodities, and the net incomes of the individuals depend on local production costs, including fixed costs and the transportation costs between the places of production to consumption. Therefore, local income depends on population densities. The economy is assumed to be in a momentary quasi-equilibrium with reference to the population distribution. The evolution of the population distribution is described by nonlinear migratory equations of motion. The driving forces within these equations are local differences in individual incomes. These motivate individual to migrate to locations of optimal income. This process leads to the evolution of spatially heterogeneous population distributions forming the settlements. © 1994.
Weidlich, W. (1994). Settlement formation at the meso-scale. Chaos, Solitons and Fractals, 4(4), 507–518. https://doi.org/10.1016/0960-0779(94)90062-0