Modeling the dynamics and spatial heterogeneity of city growth

Abstract We propose a systems model for urban population growth dynamics, disaggregated at the county scale, to explicitly acknowledge inter and intra-city movements. Spatial and temporal heterogeneity of cities are well captured by the model parameters estimated from empirical data for 2005–2019 domestic migration in the U.S. for 46 large cities. Model parameters are narrowly dispersed over time, and migration flows are well-reproduced using time-averaged values. The spatial distribution of population density within cities can be approximated by negative exponential functions, with exponents varying among cities, but invariant over the period considered. The analysis of the rank-shift dynamics for the 3100+ counties shows that the most and least dense counties have the lowest probability of shifting ranks, as expected for ‘closed’ systems. Using synthetic rank lists of different lengths, we find that counties shift ranks gradually via diffusive dynamics, similar to other complex systems.