RT Journal Article
SR Electronic
T1 Urban growth and the emergent statistics of cities
JF Science Advances
JO Sci Adv
FD American Association for the Advancement of Science
SP eaat8812
DO 10.1126/sciadv.aat8812
VO 6
IS 34
A1 Bettencourt, Luis M. A.
YR 2020
UL http://advances.sciencemag.org/content/6/34/eaat8812.abstract
AB Urban theory models cities as spatial equilibria to derive their aggregate properties as functions of extensive variables, such as population size. However, this assumption seems at odds with citiesâ€™ most interesting properties as engines of fast and variable processes of growth and change. Here, we build a general statistical dynamics of cities across scales, from single agents to entire urban systems. We include agentsâ€™ strategic behavior to produce predictable growth rates, which requires balancing relative incomes and costs over time. We implement these dynamics using stochastic differential equations and control theory to demonstrate a number of general emergent properties of cities deriving from limit theorems applied to growth rates. This framework establishes necessary conditions for scaling to be conserved by urban dynamics and shows how exponent corrections can be calculated. These ideas are tested using stochastic simulations and a long timeseries for 382 US Metropolitan Areas over nearly five decades.