Investigations to the Dynamics of City-Size Distribution Containing Birth and Death Factors

A kinetic model, which involves emigration, immigration, birth, death, and fluctuation terms, is utilized to investigate the evolution of city-size distribution. The Boltzmann-type equation and the corresponding Fokker–Planck equation are obtained to analyze the urban size distribution. Three different population variable functions, containing both birth and death rates, are considered. For each population variable function, the closed form of its stationary solution is derived. It is found that the size of urban population distribution follows a power law. Numerical simulation illustrates the correctness of the results.