Ebook: Nonlinear Difference Equations: Theory with Applications to Social Science Models

It is generally acknowledged that deterministic formulations of dy­ namical phenomena in the social sciences need to be treated differently from similar formulations in the natural sciences. Social science phe­ nomena typically defy precise measurements or data collection that are comparable in accuracy and detail to those in the natural sciences. Con­ sequently, a deterministic model is rarely expected to yield a precise description of the actual phenomenon being modelled. Nevertheless, as may be inferred from a study of the models discussed in this book, the qualitative analysis of deterministic models has an important role to play in understanding the fundamental mechanisms behind social sci­ ence phenomena. The reach of such analysis extends far beyond tech­ nical clarifications of classical theories that were generally expressed in imprecise literary prose. The inherent lack of precise knowledge in the social sciences is a fun­ damental trait that must be distinguished from "uncertainty. " For in­ stance, in mathematically modelling the stock market, uncertainty is a prime and indispensable component of a model. Indeed, in the stock market, the rules are specifically designed to make prediction impossible or at least very difficult. On the other hand, understanding concepts such as the "business cycle" involves economic and social mechanisms that are very different from the rules of the stock market. Here, far from seeking unpredictability, the intention of the modeller is a scientific one, i. e.

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This book presents a rare mix of the latest mathematical theory and procedures in the area of nonlinear difference equations and discrete dynamical systems, together with applications of this theory to models in economics and other social sciences The theoretical results include not only familiar topics on chaos, bifurcation stability and instability of cycles and equilibria, but also some recently published and some as yet unpublished results on these and related topics (e.g., the theory of semiconjugates). In addition to rigorous mathematical analysis, the book discusses several social science models and analyzes some of them in substantial detail. This book is of potential interest to professionals and graduate students in mathematics and applied mathematics, as well as researchers in social sciences with an interest in the latest theoretical results pertaining to discrete, deterministic dynamical systems.

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This book presents a rare mix of the latest mathematical theory and procedures in the area of nonlinear difference equations and discrete dynamical systems, together with applications of this theory to models in economics and other social sciences The theoretical results include not only familiar topics on chaos, bifurcation stability and instability of cycles and equilibria, but also some recently published and some as yet unpublished results on these and related topics (e.g., the theory of semiconjugates). In addition to rigorous mathematical analysis, the book discusses several social science models and analyzes some of them in substantial detail. This book is of potential interest to professionals and graduate students in mathematics and applied mathematics, as well as researchers in social sciences with an interest in the latest theoretical results pertaining to discrete, deterministic dynamical systems.
Content:
Front Matter....Pages i-xv
Front Matter....Pages 1-1
Preliminaries....Pages 3-11
Dynamics on the Real Line....Pages 13-69
Vector Difference Equations....Pages 71-164
Higher Order Scalar Difference Equations....Pages 165-239
Front Matter....Pages 241-241
Chaos and Stability in Some Models....Pages 243-337
Additional Models....Pages 339-366
Back Matter....Pages 367-388

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This book presents a rare mix of the latest mathematical theory and procedures in the area of nonlinear difference equations and discrete dynamical systems, together with applications of this theory to models in economics and other social sciences The theoretical results include not only familiar topics on chaos, bifurcation stability and instability of cycles and equilibria, but also some recently published and some as yet unpublished results on these and related topics (e.g., the theory of semiconjugates). In addition to rigorous mathematical analysis, the book discusses several social science models and analyzes some of them in substantial detail. This book is of potential interest to professionals and graduate students in mathematics and applied mathematics, as well as researchers in social sciences with an interest in the latest theoretical results pertaining to discrete, deterministic dynamical systems.
Content:
Front Matter....Pages i-xv
Front Matter....Pages 1-1
Preliminaries....Pages 3-11
Dynamics on the Real Line....Pages 13-69
Vector Difference Equations....Pages 71-164
Higher Order Scalar Difference Equations....Pages 165-239
Front Matter....Pages 241-241
Chaos and Stability in Some Models....Pages 243-337
Additional Models....Pages 339-366
Back Matter....Pages 367-388
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