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Time Evolution of City Distributions in Germany

Group-Theoretic Spectrum Analysis

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Abstract

This paper aims to capture characteristic agglomeration patterns in population data in Germany from 1987 to 2011, encompassing pre- and post-unification periods. We utilize a group-theoretic double Fourier spectrum analysis procedure (Ikeda et al. 2018) as a systematic means to capture characteristic agglomeration patterns in population data. Among a plethora of patterns to be self-organized from a uniform state, we focus on a megalopolis pattern, a rhombic pattern, and a core–satellite pattern (a downtown surrounded by hexagonal satellite cities). As the technical contribution of this paper, we newly introduce a principal vector as a superposition of these patterns in order to grasp the multi-scale nature of agglomerations. Benchmark spectra for these patterns are advanced and are found in the population data of Germany in 2011. An incremental population is investigated using this principal vector to successfully detect a shift of predominant population increase/decrease patterns in the pre- and post-unification periods.

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Notes

  1. These are so-called isotypic components in group-theoretic bifurcation theory (Golubitsky et al. 1988).

  2. Although the population map in Eastern Germany is not fully covered due to the lack of data in 1987, it does not affect the results of this section.

  3. In this figure and in the remainder of this paper, the squared magnitude \(||\varvec{q}^{(1)}||^2\) for the uniform distribution is suppressed since such a distribution is not of interest in the present study.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Tohoku University, Sendai, 980-8579, Aoba, Japan

    Kiyohiro Ikeda & Minoru Osawa

  2. Institute of Science and Engineering, Kanazawa University, Kanazawa, 920-1192, Kakuma, Japan

    Yuki Takayama

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  1. Kiyohiro Ikeda
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  2. Minoru Osawa
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  3. Yuki Takayama
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Correspondence to Kiyohiro Ikeda.

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Grant-in-Aid for JSPS 18K04380/18K18874/19K15108 is greatly appreciated.

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Ikeda, K., Osawa, M. & Takayama, Y. Time Evolution of City Distributions in Germany. Netw Spat Econ 22, 125–151 (2022). https://doi.org/10.1007/s11067-021-09557-2

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