A chronotopic model of mobility in urban spaces

In this paper, we propose an urban mobility model based on individual stochastic dynamics driven by the chronotopic action with a deterministic public transportation network. Such a model is inspired by a new approach to the problem of urban mobility that focuses the attention to the individuals and considers the presence of random components and attractive areas (chronotopoi), an essential ingredient to understand the citizens dynamics in the modern cities. The computer simulation of the model allows virtual experiments on urban spaces that describe the mobility as the evolution of a non-equilibrium system. In the absence of chronotopoi the relaxation to a stationary state is studied by the mean-field equations. When the chronotopoi are switched on the different classes of people feel an attraction toward the chronotopic areas proportional to a power law of the distance. In such a case, a theoretical description of the average evolution is obtained by using two diffusion equations coupled by local mean-field equations.