Institute for Mathematical Behavioral Sciences

Oscillatory patterns of expansion/contraction have long characterized the dynamics of demographic, economic, and political processes of human societies, including those of exchange economies and globalization. Major perturbations in city-size distributions are shown to exist for major regions in Eurasia in the last millennium and to exhibit some of the characteristics of cyclical oscillations on the scale of 100s of years as well as longer fluctuations, from 400 up to 800 years, between periods of major collapse, often punctuated by lesser collapse. Variations in timing, irregularities in amplitudes, and ups and downs in our measures appear to correlate with some of the peaks and troughs in urban population growth and show long-cycle correlations with J.S. Lee’s (1931) sociopolitical instability (SPI) data on the durations of internecine wars for China. We focus here on central civilization within the world cities database, including China and Europe, and the Mid-Asian region between. These data are likely to reflect changes in the macro regions connected by trade networks, where we would expect synchronization. Our interpretation of city-size distribution oscillations is that they follow, with generational time lags, rises and falls in the expansion/contraction of multi-connected trade network macro zones, with Zipfian city-size hierarchies tending to rise with trade network expansions and fall with contractions. City system rise and fall also tend to couple with oscillations of population relative to resources interacting with SPI in total cycles that average about 220 years. Time-lagged synchronies in the dating of phases for city distributions in different regions that are connected by multiple routes of trade, as noted tentatively by Chase-Dunn and Manning (2002:21), at least in the rising and more Zipfian phase, support the existence of city-system rise and fall cycling. We find evidence that rise and fall in Silk Road connectivities between China and Europe had time lagged effects on the growth of power law tails in European urban hierarchies; that changes in Mid-Asia city distributions led weakly those in China while those in China led strongly those in Europe, at different time lags.