We provide an analytical approach that facilitates understanding the bifurcation mechanism of a wide class of economic models involving spatial agglomeration of economic activities. The proposed method overcomes the limitations of the Turing (1952) approach that has been used to analyze the emergence of agglomeration in the multi-regional core-periphery (CP) model of Krugman (1993Krugman ( , 1996. In other words, the proposed method allows us to examine whether agglomeration of mobile factors emerges from a uniform distribution and to analytically trace the evolution of spatial agglomeration patterns (i.e., bifurcations from various polycentric patterns as well as a uniform pattern) that these models exhibit when the values of some structural parameters change steadily. Applying the proposed method to the multi-regional CP model, we uncover a number of previously unknown properties of the CP model, and notably, the occurrence of "spatial period doubling bifurcation" in the CP model is proved.

This study examines effects of bottleneck congestion and an optimal time-varying congestion toll on the spatial structure of cities. To this end, we develop a model in which heterogeneous commuters choose departure times from home and residential locations in a monocentric city with a bottleneck located between a central downtown and an adjacent suburb. We then show three properties of our model by analyzing equilibrium with and without congestion tolling.First, commuters with a higher value of travel time choose to live closer to their workplace.Second, congestion tolling causes population to increase in the suburb and generates urban sprawl. Third, commuters with a higher (lower) value of travel time gain (lose) from imposing the congestion toll without toll-revenue redistribution. Our findings are opposite to the standard results of traditional location models, which consider static traffic flow congestion, and differ fundamentally from the results obtained by Arnott (1998), who considers homogeneous commuters.JEL classification: D62; R21; R41; R48

The mechanism of self‐organization of agglomerations in a long narrow economy of a new economic geography model is elucidated by a theoretical comparative study with a racetrack economy. Computational bifurcation theory is used to systematically obtain the equilibria of these economies. A chain of spatially repeated core–periphery patterns à la Christaller and Lösch emerges when agglomeration forces are large. Peripheral zones are enlarged recurrently to engender an agglomeration shadow en route to an atomic mono‐center. A megalopolis with two core places connected by an industrial belt emerges when agglomeration forces are small.

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This paper elucidates which agglomeration patterns exist in two‐dimensional economic space and how such patterns appear stably. Hexagonal lattices, that with and that without a boundary, are advanced, respectively, as practical and theoretical spatial platforms of economic activities. Agglomeration patterns on these lattices include hexagons in central place theory, but also encompass megalopolis and racetrack‐shaped decentralization. As the transport cost decreases, stable economic agglomeration undergoes the formation of the smallest hexagon and transition to patterns with larger market areas, often undergoing downtown decay but finally leading to a megalopolis. Formulas for break points are provided in an economic geography model.

Since the seminal work of Henderson (1981), a number of studies examined the effect of staggered work hours by analyzing models of work start time choice that consider the trade-off between negative congestion externalities and positive production externalities. However, these studies described traffic congestion using flow congestion models. This study develops a model of work start time choice with bottleneck congestion and discloses the intrinsic properties of the model. To this end, this study extends Henderson's model to incorporate bottleneck congestion. By utilizing the properties of a potential game, we characterize equilibrium and optimal distributions of work start times. We also show that Pigouvian tax/subsidy policies generally yield multiple equilibria and that the first-best optimum must be a stable equilibrium under Pigouvian policies, whereas the secondbest optimum in which policymakers cannot eliminate queuing congestion can be unstable.JEL classification: C62; C72; C73; D62; R41; R48

Harris and Wilson (1978)'s retail location model is one of the pioneering works in regional sciences on the combination of the "fast" and "slow" dynamic describing spatial pattern formation processes in the economic landscape, which is a current well-established modeling technique. Although proposed some time ago, the comparative static (bifurcation) properties of the model have not yet been sufficiently explored. We employ a simple analytical approach developed by Akamatsu et al. (2012) to reveal previously unknown bifurcation properties of the model in a space with a large number of locations. It is analytically shown that the evolutionary path of spatial structure exhibits a remarkable property, namely "spatial perioddoubling cascade," which we cannot observe in the popular two-location setup. We also discuss strong linkages between the model and the models of "new economic geography" regarding the modeling strategies and their bifurcation properties.

Self-organization of hexagonal distributions of cities of various sizes in Southern Germany is envisaged in central place theory. Yet scientific verification of this theory has been lacking over the years. To scientifically support this theory, we propose a group-theoretic double Fourier spectrum analysis procedure that can detect self-organizing patterns bifurcating from a uniform state. This procedure is reinforced by the optimization of the choice of an analysis domain and the spatial eigen-decomposition to capture agglomeration effects. Strong power spectra for hexagonal networks of cities were detected by the procedure for population data in Southern Germany. Moreover, a gigantic hexagonal distribution of cities in Eastern USA was found as an assemblage of a series of hexagonal networks. The amazing geometrical regularity observed in this distribution manifests the existence of such distribution in the real world, thereby underpinning central place theory.