Dynamics of Cities

Abstract

This study investigates city dynamics employing a nonextensive diffusion equation suited for addressing diffusion within a fractal medium, where the nonadditive parameter, $q$, plays a relevant role. The findings demonstrate the efficacy of this approach in determining the relation between the fractal dimension of the city, the allometric exponent and $q$, and elucidating the stationary phase of urban evolution. The dynamic methodology facilitates the correlation of the fractal dimension with both the entropic index and the urban scaling exponent identified in data analyses. The results reveal that the scaling behaviour observed in cities aligns with the fractal dimension measured through independent methods. Moreover, the interpretation of these findings underscores the intimate connection between the fractal dimension and social interactions within the urban context. This research contributes to a deeper comprehension of the intricate interplay between human behaviour, urban dynamics, and the underlying fractal nature of cities.

Keywords: Allometric scaling, fractal dimension, Dynamic Equation, Nonlinear Diffusion, Nonextensive Systems, Tsallis Statistics