Time-series analysis of clusters in city size distributions

Complex systems, such as urban systems, emerge unpredictably without the influence of central control as a result of adaptive behaviour by their component, interacting agents. This paper analyses city size distributions, by decade, from the south-western region of the United States for the years 1890-1990. It determines if the distributions were clustered and documents changes in the pattern of clusters over time. Clusters were determined utilising a kernel density estimator and cluster analysis. The data were clustered as determined by both methods. The analyses identified 4-7 clusters of cities in each of the decades analysed. Cities cluster into size classes, suggesting variability in growth rates at different scales.