Hexagonal distributions of cities of various sizes in Southern Germany are envisaged in central place theory. Yet scientific verification of this theory has been lacking. To scientifically support this theory, we propose a group-theoretic double Fourier spectrum analysis procedure that can...

Cities in Southern Germany are envisaged to form hexagonal distributions in central place theory; however, rigorous verification of this theory has been lacking over years. To support this theory, we introduce a group-theoretic Fourier spectrum analysis that can detect geometrical patterns of...

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...

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...

We investigate economic agglomerations in a long narrow economy, in which discrete locations are evenly spread over a line segment. The bifurcation mechanism of a monocentric city at the center is analyzed analytically to show how and where satellite cities form. This is an important step to...

Racetrack economy is a conventional spatial platform for economic agglomeration in spatial economy models. Studies of this economy up to now have been conducted mostly on $2^k$ cities, for which agglomerations proceed via so-called spatial period doubling bifurcation cascade. This paper aims at...