Nonlinear Difference Equations: Theory with Applications to Social Science Models / Edition 1

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Overview

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chaos, bifurcation stability and instability of cycles and equilibria, but also some recently published and some as yet unpublished results on these and related topics (e.g., the theory of semiconjugates).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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Table of Contents

Preface. Acknowledgements. Part I: Theory. 1. Preliminaries. 2. Dynamics on the real line. 1. Equilibria and their stability. 2. Cycles and limit cycles. 3. Elementary bifurcations. 3: Vector Tangent Equations. 1. Stability. 2. Semiconjugates of maps on the line. 3. Chaotic maps. 4. Polymodal systems and thresholds. 4: Higher Order Scalar Difference Equations. 1. Boundedness and persistent oscillations. 2. Permanence. 3. Global attractivity and related results. Part II: Applications to CSocial Science Models. 5: Chaos and Stability in Some Models. 1. The accelerator-multiplier business cycle models. 2. A productivity growth model. 3. Chaos and competition in a model of consumer behavior. 4. An overlapping generations consumption-loan model. 5. A dynamic model of consumer demand. 6. A bimodal model of combat. 6: Additional Models. 1. Addiction and habit formation. 2. Budgetary competition. 3. Cournot duopoly. 4. Chaos in real exchange rates. 5. Real wages and mode switching. 6. Chaos in a dynamic equilibrium model. 7. Oscillatory behavior in an OLG model. 8. Attractor basins and critical curves in two models. 9. Reducing inflation: gradual vs. shock treatment. 10. Walrasian tatonnement with adaptive expectations. 11. Socio-spatial dynamics. 12. Models of arms race. Bibliography. Index.
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