Overview
- 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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Table of contents (9 chapters)
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Front Matter
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Economic Agglomeration and Bifurcation: Introduction
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Front Matter
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Theory of Economic Agglomeration on Hexagonal Lattice
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Front Matter
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Back Matter
Keywords
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)Authors and Affiliations
Bibliographic Information
Book Title: Bifurcation Theory for Hexagonal Agglomeration in Economic Geography
Authors: Kiyohiro Ikeda, Kazuo Murota
DOI: https://doi.org/10.1007/978-4-431-54258-2
Publisher: Springer Tokyo
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer Japan 2014
Hardcover ISBN: 978-4-431-54257-5Published: 26 November 2013
Softcover ISBN: 978-4-431-56338-9Published: 23 August 2016
eBook ISBN: 978-4-431-54258-2Published: 08 November 2013
Edition Number: 1
Number of Pages: XVII, 313
Number of Illustrations: 54 b/w illustrations, 15 illustrations in colour
Topics: Engineering Economics, Organization, Logistics, Marketing, Data-driven Science, Modeling and Theory Building, Mathematical Modeling and Industrial Mathematics, Mathematics in the Humanities and Social Sciences, Population Economics