Bifurcation Theory for Hexagonal Agglomeration in Economic Geography

  • Kiyohiro Ikeda
  • Kazuo Murota

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Economic Agglomeration and Bifurcation: Introduction

    1. Front Matter
      Pages 1-1
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 29-75
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 77-103
  3. Theory of Economic Agglomeration on Hexagonal Lattice

    1. Front Matter
      Pages 105-105
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 107-124
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 125-145
    4. Kiyohiro Ikeda, Kazuo Murota
      Pages 147-174
    5. Kiyohiro Ikeda, Kazuo Murota
      Pages 175-202
    6. Kiyohiro Ikeda, Kazuo Murota
      Pages 273-306
  4. Back Matter
    Pages 307-313

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.


Core-periphery Model Economic Agglomeration Equivariant Bifurcation Theory Group-theoretic Bifurcation Theory Hexagonal Distribution

Authors and affiliations

  • Kiyohiro Ikeda
    • 1
  • Kazuo Murota
    • 2
  1. 1.Civil and Environmental Engineering Graduate School of EngineeringTohoku UniversitySendaiJapan
  2. 2.Information Science and TechnologyThe University of TokyoBunkyo-kuJapan

Bibliographic information

  • DOI
  • Copyright Information Springer Japan 2014
  • Publisher Name Springer, Tokyo
  • eBook Packages Engineering
  • Print ISBN 978-4-431-54257-5
  • Online ISBN 978-4-431-54258-2
  • Buy this book on publisher's site
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