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

Akamatsu, Takashi and Osawa, Minoru 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 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 period- doubling 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.

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