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

Abstract

The orientation and progress of spatial agglomeration for Krugman's core-periphery model are investigated in this paper. Possible agglomeration patterns for a system of cities spread uniformly on a circle are set forth theoretically. For example, a possible and most likely course predicted for eight cities is a gradual and successive oneconcentration into four cities and then into two cities en route to a single city. The existence of this course is ensured by numerical simulation for the model. Such gradual and successive agglomeration, which is called spatial-period doubling, presents a sharp contrast with the agglomeration of two cities, for which spontaneous concentration to a single city is observed in models of various kinds. It exercises caution about the adequacy of the two cities as a platform of the spatial agglomerations and demonstrates the need of the study on a system of cities.

A probabilistic modeling approach to the detection of industrial agglomerations

“…to directly identify the spatial patterns of industrial agglomerations on a map, and test the hypotheses implied by the recent theoretical developments on economic agglomerations under many-region/continuous location space (e.g., Fujita et al [8], Tabuchi and Thisse [30], Hsu [10], Ikeda et al [12]). Below, we touch on two areas where initial investigations are already under way.…”

“…To motivate our approach to cluster detection, we begin by observing that recent theoretical results on equilibrium location patterns in continuous space (e.g., Hsu [10], Ikeda et al [12]) suggest that there is remarkable commonality among possible equilibrium patterns of agglomeration within each industry. In particular, the number, size and spacing of agglomerations are shown to be well preserved under a variety of stable equilibria.…”

“…12 In this context, if the length, l(ρ), of path, ρ = (r 1 , r 2 , ..., r n ), is now taken to be the sum of travel distances on each of its links, i.e.,…”

On the spatial scale of industrial agglomerations

“…Within the NEG, a number of models have been developed to explain the spacing between individual clusters for a given industry (e.g., Krugman [27] [22], Akamatsu et al [2]). From the viewpoint of general equilibrium theory, these models predict whether an agglomeration of industrial firms will be viable at a given location, depending on how other clusters of the same industry (as well as population) are distributed over the location space.…”

Origin, spatial pattern, and evolution of urban system: Testing a hypothesis of “urban tree”

“…The evolution of urban spatial structure is usually studied by remote sensing techniques or spatial land use change models (Krehl, Siedentop, Taubenb€ ock, & Wurm, 2016;Van de Voorde et al, 2016), the (population or economic indicators) modeling method and graph theory analysis. The generalized equilibrium model (Berliant & Wang, 2008), logical model (Ikeda, Akamatsu, & Kono, 2012) and gravity model (Wang, Deng, Su, & Song, 2014) have been widely applied in this field. Since the evolution of spatial structure of urban system is closely related to population and economic factors (Chadchan & Shankar, 2012;Dong et al, 2014), population and economic indicators are often used to describe the urban system growth and decline (Filion, 2010;Li, Huang, & Wang, 1998).…”