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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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Contenuti
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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Nonlinear Difference Equations: Theory with Applications to Social Science Models (Mathematical Modelling: Theory and Applications, 15)
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Hardcover. Condizione: new. Hardcover. This text 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 (for example, 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9781402011160
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Nonlinear Difference Equations: Theory with Applications to Social Science Models (Mathematical Modelling: Theory and Applications, 15)
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 408 pp. Englisch. Codice articolo 9781402011160
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Nonlinear Difference Equations: Theory with Applications to Social Science Models
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Buch. Condizione: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 408 pp. Englisch. Codice articolo 9781402011160
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Nonlinear Difference Equations : Theory with Applications to Social Science Models
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9781402011160
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