Bifurcation theory for hexagonal agglomeration in economic geography [electronic resource] / Kiyohiro Ikeda, Kazuo Murota.

Bifurcation theory for hexagonal agglomeration in economic geography [electronic resource] / Kiyohiro Ikeda, Kazuo Murota.

9784431542582 electronic book
4431542582 electronic book
9784431542575

Tokyo : Springer, 2014.

English

1 online resource.

10.1007/978-4-431-54258-2 doi

HF1025

330.90015118

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.

Includes bibliographical references and index.

Access limited to authorized users.

Description based on print version record.

Online Resources > Ebooks
All Resources