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Break and sustain bifurcations of S_N-invariant equidistant economy

Author

Listed:
  • Aizawa, Hiroki
  • Ikeda, Kiyohiro
  • Osawa, Minoru
  • José M, Gasper
Abstract
This paper aims at the elucidation of the bifurcation mechanism of an equidistant economy in Economic Geography. An attention is paid to the existence of invariant solutions that retain their spatial patterns when the bifurcation parameter changes. Theoretical results on symmetrybreaking bifurcation of the symmetric group SN, which describes the symmetry of this economy, is combined with the mechanism of sustain bifurcation of invariant patterns that is inherent to the economy. The stability of bifurcating branches is investigated theoretically to demonstrate that most of them are asymptotically unstable. Among a plethora of theoretically possible spatial patterns, those which actually become stable for spatial economic models are investigated numerically. The solution curves of the economy are shown to display a complicated mesh-like structure, which looks like threads of warp and weft.

Suggested Citation

  • Aizawa, Hiroki & Ikeda, Kiyohiro & Osawa, Minoru & José M, Gasper, 2019. "Break and sustain bifurcations of S_N-invariant equidistant economy," MPRA Paper 97654, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:97654
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    File URL: https://mpra.ub.uni-muenchen.de/97761/1/MPRA_paper_97654.pdf
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    References listed on IDEAS

    as
    1. José M. Gaspar & Sofia B. S. D. Castro & João Correia-da-Silva, 2018. "Agglomeration patterns in a multi-regional economy without income effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 863-899, December.
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    4. José Gaspar & Sofia Balbina Santos Dias de Castro & João Correia da Silva, 2013. "The Footloose Entrepreneur Model with 3 Regions," FEP Working Papers 496, Universidade do Porto, Faculdade de Economia do Porto.
    5. Puga, Diego, 1999. "The rise and fall of regional inequalities," European Economic Review, Elsevier, vol. 43(2), pages 303-334, February.
    6. Richard Baldwin & Rikard Forslid & Philippe Martin & Gianmarco Ottaviano & Frederic Robert-Nicoud, 2005. "Economic Geography and Public Policy," Economics Books, Princeton University Press, edition 1, number 7524.
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    8. Oyama, Daisuke, 2009. "Agglomeration under forward-looking expectations: Potentials and global stability," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 696-713, November.
    9. Zeng, Dao-Zhi & Uchikawa, Tomohiro, 2014. "Ubiquitous inequality: The home market effect in a multicountry space," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 225-233.
    10. Richard Baldwin & Rikard Forslid & Philippe Martin & Gianmarco Ottaviano & Frederic Robert-Nicoud, 2005. "Economic Geography and Public Policy," Economics Books, Princeton University Press, edition 1, number 7524.
    11. José Gaspar & Kiyohiro Ikeda & Mikihasa Onda, 2019. "Global bifurcation mechanism and local stability of identical and equidistant regions," Working Papers de Economia (Economics Working Papers) 04, Católica Porto Business School, Universidade Católica Portuguesa.
    12. Commendatore, Pasquale & Kubin, Ingrid & Sushko, Iryna, 2015. "Typical bifurcation scenario in a three region identical New Economic Geography model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 63-80.
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    Cited by:

    1. Gaspar, José M. & Ikeda, Kiyohiro & Onda, Mikihasa, 2021. "Global bifurcation mechanism and local stability of identical and equidistant regions: Application to three regions and more," Regional Science and Urban Economics, Elsevier, vol. 86(C).

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    More about this item

    Keywords

    Bifurcation; equidistant economy; group-theoretic bifurcation theory; invariant pattern; replicator dynamics; spatial economic model; stability;
    All these keywords.

    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)

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    This paper has been announced in the following NEP Reports:

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