Nonlinear Difference Equations: Theory with Applications to Social Science Models

ISBN-13: 9789048162154 / Angielski / Miękka / 2010 / 388 str.

H. Sedaghat

Opis

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.

Spis treści

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.