IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/86923.html
   My bibliography  Save this paper

Bifurcation theory of a racetrack economy in a spatial economy model

Author

Listed:
  • Ikeda, Kiyohiro
  • Onda, Mikihisa
  • Takayama, Yuki

Abstract

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 the elucidation of agglomeration mechanisms of the racetrack economy in a general setting of an arbitrary number of cities. First, an attention was paid to the existence of invariant solutions that retain their spatial distributions when the transport cost parameter is changed. A complete list of possible invariant solutions, which are inherent for replicator dynamics and are dependent on the number of cities, is presented. Next, group-theoretic bifurcation theory is used to describe bifurcation from the uniform state, thereby presenting an insightful information on spatial agglomerations. Among a plethora of theoretically possible invariant solutions, those which actually become stable for spatial economy models are obtained numerically. Asymptotic agglomeration behavior when the number of cities become very large is studied.

Suggested Citation

  • Ikeda, Kiyohiro & Onda, Mikihisa & Takayama, Yuki, 2018. "Bifurcation theory of a racetrack economy in a spatial economy model," MPRA Paper 86923, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:86923
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/86923/1/MPRA_paper_86923.pdf
    File Function: original version
    Download Restriction: no

    More about this item

    Keywords

    Bifurcation; Economic agglomeration; Racetrack economy; Replicator dynamics; Spatial economy model;

    JEL classification:

    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:86923. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.