Chapter 30 Decision-based modelling of complex spatial systems
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It is shown that the Master equation as unifying framework leads to a better understanding of the complexity of the dynamics of interacting urban and regional systems. Without any assumption concerning the distribution of uncertainties a generalized Master equation decision model of interacting populations is obtained. Migratory decisions of individuals lead to population flows on the macro level. In the long run, in case of decreasing marginal attractiveness with settlement size a scale invariant Pareto distribution is obtained as an attractor. In this case the spatial system fulfils the condition of self-organized criticality (SOC). The necessary conditions to obtain the observed rank-size distribution leads to restrictive conditions for the agglomeration term of the spatial attractiveness function. This has an impact on the explicit form of the Master equation migration model, and vice versa, on the stability conditions of the settlement system.

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