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This book presents the theory and practical applications of the
Master equation approach, which provides a powerful general
framework for model building in a variety of disciplines. The aim
of the book is to not only highlight different mathematical
solution methods, but also reveal their potential by means of
practical examples. Part I of the book, which can be used as a
toolbox, introduces selected statistical fundamentals and solution
methods for the Master equation. In Part II and Part III, the
Master equation approach is applied to important applications in
the natural and social sciences. The case studies presented mainly
hail from the social sciences, including urban and regional
dynamics, population dynamics, dynamic decision theory, opinion
formation and traffic dynamics; however, some applications from
physics and chemistry are treated as well, underlining the
interdisciplinary modelling potential of the Master equation
approach. Drawing upon the author's extensive teaching and research
experience and consulting work, the book offers a valuable guide
for researchers, graduate students and professionals alike.
This book presents the theory and practical applications of the
Master equation approach, which provides a powerful general
framework for model building in a variety of disciplines. The aim
of the book is to not only highlight different mathematical
solution methods, but also reveal their potential by means of
practical examples. Part I of the book, which can be used as a
toolbox, introduces selected statistical fundamentals and solution
methods for the Master equation. In Part II and Part III, the
Master equation approach is applied to important applications in
the natural and social sciences. The case studies presented mainly
hail from the social sciences, including urban and regional
dynamics, population dynamics, dynamic decision theory, opinion
formation and traffic dynamics; however, some applications from
physics and chemistry are treated as well, underlining the
interdisciplinary modelling potential of the Master equation
approach. Drawing upon the author's extensive teaching and research
experience and consulting work, the book offers a valuable guide
for researchers, graduate students and professionals alike.
In part I of this book a dynamic migratory model connecting the
microlevel of individual migration trends with the macrolevel of
interregional migration is developed. Its derivation makes use of
the master equation method. Applying a ranking regression analysis,
the trend parameters of the model are correlated to regional
socio-economic key factors. In part II the model is applied to
interregional migration within the countries Federal Republic of
Germany, Canada, France, Israel, Italy and Sweden. In part III a
comparative analysis of the results is given. In part IV a
selfcontained derivation of the master equation and of solutions
relevant for the migratory system is given, the ranking regression
analysis is exemplified and a computer program for the estimation
of trendparameters is added.
Gone are the days when mobility was nearly always a question of
having a vehicle. Today the issue of road capacity is becoming ever
more pressing. Even the safest, most comfortable and 100%
emissions-free vehicle is only of limited use if it is stuck in a
traffic jam. Mobility is a key human need and an important factor
in the economy. It is a matter of logic that a com pany like
DaimlerChrysler should make every endeavor to safeguard mo bility,
thereby fulfilling humanity's economic, social and environmental
needs. Nonetheless, traffic and mobility problems are the
inevitable result of a concentration of people and markets. Bombay,
Lagos, Shanghai, Jakarta, Sao Paulo, Cairo, Mexico City - virtually
half of the world's population is urban-based, and the majority
live in the metropolitan regions of the Third World. The
mega-cities in the so-called developing nations are facing a
dramatic increase in traffic levels. Gridlock looms on the horizon.
Should traffic-choked streets become a permanent and daily
occurrence, economic development will be held in check and
pollution will spiral."
The articles collected in this volume have two features in common:
they wantto integrate economics, demography and geography, and they
want to overcome the stationary approach in modelling in favour of
a dynamic one. The book is subdivided into three parts, where Part
I is focussing on economic evolution, Part II on geographical
development and Part III is related to demographic change. The
present volume aims at providing a new look at this triangle in
view of the classical background of discussions by introducing new
research ideas focussing in nonlinear dynamics and stochastic
modelling. Thus the main purpose of this book is to make a
contribution to the interdisciplinary work needed to integrate the
effortsbetween these three research fields and to serve as a
research source in demonstrating the current state of art in
dynamic modelling. The book isaddressed to social scientists in
general, and those in particular with a background in economics,
geographics and demographics. It should also be of interest to
mathematicians, physicists, and systems analysts interested in
model building and applications of nonlinear dynamics.
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