Spatial period-doubling agglomeration of a core-periphery model with a system of cities

The progress of spatial agglomeration of Krugman's core-periphery model is investigated by comparative static analysis of stable equilibria with respect to transport costs. We set forth theoretically possible agglomeration (bifurcation) patterns for a system of cities spread uniformly on a circle. A possible and most likely course predicted is a gradual and successive one, which is called spatial period doubling. For example, eight cities concentrate into four cities and then into two cities en route to the formation of a single city. The existence of this course is ensured by numerical simulation for the model. Such a gradual and successive agglomeration presents a sharp contrast to the agglomeration of two cities, for which spontaneous concentration to a single city is observed in core-periphery models of various kinds. Other bifurcations that do not take place in two cities, such as period tripling, are also observed. The need for study of a system of cities has thus been demonstrated.