The temporal evolution of the city size distribution

We present an application of a growth model for a system of cities. This computer model simulates the evolution of systems with measurable entities (e.g. city size), and takes into account the growth of the entities in terms of size and number. It includes a random multiplicative process for the growth of individual entities and for the creation of new ones. We use a new mathematical expression with a positive exponent α (which we call the 'shape exponent') and additional three parameters, to describe the dynamics of the systems' size distributions through time. We compare the changes of a real system of cities and the model's results quantitatively and qualitatively. Our findings suggest that there is a good agreement at the macro level between the model and the real data.