Nonlinearity, Chaos, and Complexity: The Dynamics of Natural and Social Systems

Paperback | August 25, 2005

byCristoforo Sergio Bertuglia, Franco Vaio

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Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique textin the midst of many current books on chaos and complexity.Part 1 deals with the mathematical model as an instrument of investigation. The general meaning of modelling and, more specifically, questions concerning linear modelling are discussed. Part 2 deals with the theme of chaos and the origin of chaotic dynamics. Part 3 deals with the theme ofcomplexity: a property of the systems and of their models which is intermediate between stability and chaos.Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.

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Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique textin the midst of many current books on chaos ...

Cristoforo Sergio Bertuglia is at Retired; formerly Professor of Urban and Regional Planning, Politecnico di Torino. Franco Vaio is at Professor of Mathematics, Politecnico di Torino.

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Format:PaperbackDimensions:402 pages, 9.21 × 6.14 × 0.86 inPublished:August 25, 2005Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:019856791X

ISBN - 13:9780198567912

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Table of Contents

ContentsPrefacePart I: Linear and nonlinear processes1.1. Introduction1.2. Modelling1.3. The Origins of System Dynamics: Mechanics1.4. Linearity in Models1.5. One of The Most Basic Natural Systems: The Pendulum1.6. Linearity as a First, Often Insufficient Approximation1.7. The Nonlinearity of Natural Processes: The Case of The Pendulum1.8. Dynamical Systems and The Phase Space1.9. Extension of The Concepts and Models Used in Physics to Economics1.10. The Chaotic Pendulum1.11. Linear Models in Social Processes: The Case of Two Interacting Populations1.12. Nonlinear Models in Social Processes: The Model of Volterra-Lotka and Some of Its Variants in Ecology1.13. Nonlinear Models in Social Processes: The Volterra-Lotka Model Applied to Urban and Regional SciencePart II: From nonlinearity to chaos2.1. Introduction2.2. Dynamical Systems and Chaos2.3. Strange and Chaotic Attractors2.4. Chaos in Real Systems and in Mathematical Models2.5. Stability in Dynamical Systems2.6. The Problem of Measuring Chaos in Real Systems2.7. Logistic Growth as A Population Development Model2.8. A Nonlinear Discrete Model: The Logistic Map2.9. The Logistic Map: Some Results of Numerical Simulations and An Application2.10. Chaos in Systems: The Main ConceptsPart III: Complexity3.1. Introduction3.2. Inadequacy of Reductionism3.3. Some Aspects of The Classical Vision of Science3.4. From Determinism to Complexity: Self-Organisation, A New Understanding of System Dynamics3.5. What is Complexity?3.6. Complexity and Evolution3.7. Complexity in Economic Processes3.8. Some Thoughts on The Meaning of 'Doing Mathematics'3.9. Digression into The Main Interpretations of The Foundations of Mathematics3.10. The Need for A Mathematics of (or for) ComplexityReferencesName IndexSubject Index