The growth equation of cities.

Nature
Vincent Verbavatz, Marc Barthelemy

Abstract

The science of cities seeks to understand and explain regularities observed in the world's major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most fundamental problem is to understand the hierarchical organization of city population and the statistical occurrence of megacities. This was first thought to be described by a universal principle known as Zipf's law1,2; however, the validity of this model has been challenged by recent empirical studies3,4. A theoretical model must also be able to explain the relatively frequent rises and falls of cities and civilizations5, but despite many attempts6-10 these fundamental questions have not yet been satisfactorily answered. Here we introduce a stochastic equation for modelling population growth in cities, constructed from an empirical analysis of recent datasets (for Canada, France, the UK and the USA). This model reveals how rare, but large, interurban migratory shocks dominate city growth. This equation predicts a complex shape for the distribution of city populations and shows that, owing to finite-time effects, Zipf's law does not hold in general, implying a more complex organization of citi...Continue Reading

References

Dec 1, 2006·Nature·Michael Batty
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tomasz Srokowski
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Bernat Corominas-Murtra, Ricard V Solé
Oct 22, 2010·Nature·Luis Bettencourt, Geoffrey West
Mar 1, 2012·Nature·Filippo SiminiAlbert-László Barabási
Aug 30, 2017·PloS One·Clémentine Cottineau

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