Bifurcation Theory for Hexagonal Agglomeration in Economic Geography

Authors: Ikeda, Kiyohiro, Murota, Kazuo

  • Attractive new research field for bifurcation theory
  • Interdisciplinary study of economic geography and nonlinear mathematics
  • Detailed theoretical and numerical recipe serviceable for wide audience
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About this book

This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distributed places, and the symmetry of this lattice is expressed by a finite group. Several mathematical methodologies indispensable for tackling the present problem are gathered in a self-contained manner. The existence of hexagonal distributions is verified by group-theoretic bifurcation analysis, first by applying the so-called equivariant branching lemma and next by solving the bifurcation equation. This book offers a complete guide for the application of group-theoretic bifurcation analysis to economic agglomeration on the hexagonal lattice.

Reviews

From the reviews:

“The monograph aims at studying city networks with the aid of bifurcation theory. … Mathematicians and physicists working in the field of representation theory should find the monograph a good advise for learning the methods and conducting research in their domain of specialization.” (Krzysztof Leśniak, zbMATH, Vol. 1286, 2014)

Table of contents (9 chapters)

  • Hexagonal Distributions in Economic Geography and Krugman’s Core–Periphery Model

    Ikeda, Kiyohiro (et al.)

    Pages 3-28

  • Group-Theoretic Bifurcation Theory

    Ikeda, Kiyohiro (et al.)

    Pages 29-75

  • Agglomeration in Racetrack Economy

    Ikeda, Kiyohiro (et al.)

    Pages 77-103

  • Introduction to Economic Agglomeration on Hexagonal Lattice

    Ikeda, Kiyohiro (et al.)

    Pages 107-124

  • Hexagonal Distributions on Hexagonal Lattice

    Ikeda, Kiyohiro (et al.)

    Pages 125-145

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-4-431-54258-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-4-431-54257-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-4-431-56338-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Bifurcation Theory for Hexagonal Agglomeration in Economic Geography
Authors
Copyright
2014
Publisher
Springer Japan
Copyright Holder
Springer Japan
eBook ISBN
978-4-431-54258-2
DOI
10.1007/978-4-431-54258-2
Hardcover ISBN
978-4-431-54257-5
Softcover ISBN
978-4-431-56338-9
Edition Number
1
Number of Pages
XVII, 313
Number of Illustrations and Tables
54 b/w illustrations, 15 illustrations in colour
Topics