Bifurcation Theory Of Pattern Formation In Economic Geography
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Bifurcation Theory Of Pattern Formation In Economic Geography
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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Nature
Release Date : 2024-11-14
Bifurcation Theory Of Pattern Formation In Economic Geography written by Kiyohiro Ikeda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-14 with Mathematics categories.
Dive into the fascinating world of economic agglomerations with this interdisciplinary study, which is perfect for readers in nonlinear mathematics, economic geography, and spatial economics. This book uniquely bridges these fields, employing group-theoretic bifurcation analysis in nonlinear mathematics to establish a robust theoretical foundation for economic geographers and mathematicians alike. Explore innovative models that describe the pattern formation in economic agglomerations through worker migration between regions. Delve into multi-regional formulations of classic economic geography models, applied to various spatial platforms such as line segments, racetracks, squares, and hexagonal lattices. This book, ideal for researchers and practitioners, offers cutting-edge insights and methodologies for understanding the complexities of spatial economic agglomerations.
Bifurcation Theory For Hexagonal Agglomeration In Economic Geography
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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-08
Bifurcation Theory For Hexagonal Agglomeration In Economic Geography written by Kiyohiro Ikeda and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-08 with Technology & Engineering categories.
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.
Imperfect Bifurcation In Structures And Materials
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Author : Kiyohiro Ikeda
language : en
Publisher: Springer Nature
Release Date : 2019-09-25
Imperfect Bifurcation In Structures And Materials written by Kiyohiro Ikeda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-25 with Science categories.
Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.
Global Analysis Of Dynamic Models In Economics And Finance
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Author : Gian Italo Bischi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-07
Global Analysis Of Dynamic Models In Economics And Finance written by Gian Italo Bischi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-07 with Business & Economics categories.
The essays in this special volume survey some of the most recent advances in the global analysis of dynamic models for economics, finance and the social sciences. They deal in particular with a range of topics from mathematical methods as well as numerous applications including recent developments on asset pricing, heterogeneous beliefs, global bifurcations in complementarity games, international subsidy games and issues in economic geography. A number of stochastic dynamic models are also analysed. The book is a collection of essays in honour of the 60th birthday of Laura Gardini.
An Economic Theory Of Cities
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Author : Wei-Bin Zhang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Economic Theory Of Cities written by Wei-Bin Zhang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
Over more than two centuries the developmentofeconomic theory has created a wide array of different concepts, theories, and insights. My recent books, Capital and Knowledge (Zhang, 1999) and A TheoryofInternational Trade (Zhang, 2000) show how separate economic theories such as the Marxian economics, the Keynesian economics, the general equilibrium theory, the neoclassical growth theory, and the neoclassical trade theory can be examined within a single theoretical framework. This book isto further expand the frameworkproposed in the previous studies. This book is a part of my economic theory with endogenous population, capital, knowledge, preferences, sexual division of labor and consumption, institutions, economic structures and exchange values over time and space (Zhang, 1996a). As an extension of the Capital and Knowledge, which is focused on the dynamics of national economies, this book is to construct a theory of urban economies. We are concerned with dynamic relations between division of labor, division ofconsumption and determination of prices structure over space. We examine dynamic interdependence between capital accumulation, knowledge creation and utilization, economicgrowth, price structuresand urban pattern formation under free competition. The theory is constructed on the basisofa few concepts within a compact framework. The comparative advantage of our theory is that in providing rich insights into complex of spatial economies it uses only a few concepts and simplified functional forms and accepts a few assumptions about behavior of consumers, producers, and institutionalstructures.
Dynamics And Bifurcation In Networks
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Author : Martin Golubitsky
language : en
Publisher: SIAM
Release Date : 2023-04-24
Dynamics And Bifurcation In Networks written by Martin Golubitsky and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-24 with Mathematics categories.
In recent years, there has been an explosion of interest in network-based modeling in many branches of science. This book synthesizes some of the common features of many such models, providing a general framework analogous to the modern theory of nonlinear dynamical systems. How networks lead to behavior not typical in a general dynamical system and how the architecture and symmetry of the network influence this behavior are the book’s main themes. Dynamics and Bifurcation in Networks: Theory and Applications of Coupled Differential Equations is the first book to describe the formalism for network dynamics developed over the past 20 years. In it, the authors introduce a definition of a network and the associated class of “admissible” ordinary differential equations, in terms of a directed graph whose nodes represent component dynamical systems and whose arrows represent couplings between these systems. They also develop connections between network architecture and the typical dynamics and bifurcations of these equations and discuss applications of this formalism to various areas of science, including gene regulatory networks, animal locomotion, decision-making, homeostasis, binocular rivalry, and visual illusions. This book will be of interest to scientific researchers in any area that uses network models, which includes many parts of biology, physics, chemistry, computer science, electrical and electronic engineering, psychology, and sociology.
Catastrophe Theory And Bifurcation Routledge Revivals
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Author : Alan Wilson
language : en
Publisher: Taylor & Francis
Release Date : 2012-11-12
Catastrophe Theory And Bifurcation Routledge Revivals written by Alan Wilson and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-12 with Mathematics categories.
Mathematical models have long been used by geographers and regional scientists to explore the working of urban and regional systems, via a system where the equilibrium point changes slowly and smoothly as the parameters change slowly and smoothly. However, this all changed with the advent of catastrophe theory and bifurcation, which enabled the development of models where a quite sudden change in the position of the equilibrium point results from a slow, small, smooth change in one or more parameters. First published in 1981, this reissue of Professor Wilson’s classic study outlines the implications of these mathematical models for geography and regional science, by way of a survey of contemporary applications.
Pattern Formation
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Author : Rebecca Hoyle
language : en
Publisher: Cambridge University Press
Release Date : 2006
Pattern Formation written by Rebecca Hoyle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
From the stripes of a zebra and the spots on a leopard's back to the ripples on a sandy beach or desert dune, regular patterns arise everywhere in nature. The appearance and evolution of these phenomena have been a focus of recent research activity across several disciplines. This book provides an introduction to the range of mathematical theory and methods used to analyze and explain these often intricate and beautiful patterns. Bringing together several different approaches, from group theoretic methods to envelope equations and theory of patterns in large-aspect ratio-systems, the book also provides insight behind the selection of one pattern over another.
Pattern Formation And Dynamics In Nonequilibrium Systems
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Author : Michael Cross
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-16
Pattern Formation And Dynamics In Nonequilibrium Systems written by Michael Cross and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-16 with Mathematics categories.
An account of how complex patterns form in sustained nonequilibrium systems; for graduate students in biology, chemistry, engineering, mathematics, and physics.
Brownian Agents And Active Particles
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Author : Frank Schweitzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-31
Brownian Agents And Active Particles written by Frank Schweitzer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-31 with Business & Economics categories.
This book lays out a vision for a coherent framework for understanding complex systems. By developing the genuine idea of Brownian agents, the author combines concepts from informatics, such as multiagent systems, with approaches of statistical many-particle physics. It demonstrates that Brownian agent models can be successfully applied in many different contexts, ranging from physicochemical pattern formation to swarming in biological systems.