Bifurcation Theory For Hexagonal Agglomeration In Economic Geography
by Kazuo Murota /
2013 / English / PDF
5.7 MB Download
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.
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.