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Harris and Wilson (1978) Model Revisited: The Spatial Period-doubling Cascade in an Urban Retail Model

Osawa, Minoru and Akamatsu, Takashi and Takayama, Yuki (2015): Harris and Wilson (1978) Model Revisited: The Spatial Period-doubling Cascade in an Urban Retail Model.

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Abstract

Harris and Wilson (1978)’s retail location model is one of the pioneering works in regional sciences. This model considers the combination of the “fast” and “slow” dynamics to describe spontaneous spatial pattern formation processes in the economic landscape. Although the model was proposed some time ago, its comparative static (bifurcation) properties 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 spatial structure’s evolutionary path exhibits a remarkable property, namely a “spatial period-doubling cascade,” which cannot be observed in the popular two-location setup. Furthermore, we discuss strong linkages between the model and “new economic geography” models in terms of their model structures and bifurcation properties. These results offer a new theoretical perspective for understanding agglomeration and spatial structure evolution.

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