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.

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."

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.

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.

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.