Urban and Hinterland Evolution under Growing Population Pressure

An integrated mathematical model for the evolution of urban structure and population ist presented. The city configuration consists of an occupation number representation of different kinds of buildings such as lodgings and factories distributed over a grid of plots, and the population configuration describes the distribution of the population between city (c) and hinterland (h). The dynamics of the total configuration is governed by motivation - dependent transition rates between neighbouring configurations. Equations of evolution on the stochastic level (masterequation) and deterministic level (quasi-meanvalue equations) can thereupon be derived. We focus on that sector of the model describing the population dynamics between hinterland (h) and city (c). Under the assumption of equal net birth rates in (c) and (h), and for given growth of the total population P(t), the dynamics of the population shares between (h) and (c) can be treated explicitely in terms of a time dependent evolution potential. One can distinguish between the two main cases of "constructive competition between (c) and (h)" and "worsening balance between (c) and (h)". In the first case a stabilisation of the population shares in c and h takes place, whereas in the second case a dramatic migratory phase transition sets in, namely a sudden rush of the population from the depleting hinterland to the overcrowding city. KEYWORDS: 1. Integration of Urban and Population Dynamics 2. Motivation Dependent Transition Rates 3. Master Equation 4. Quasimeanvalue Equations 5. Migratory Phase-Transitions