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

by Cristoforo Sergio Bertuglia, Franco Vaio

Overview

Covering a broad range of topics, this text provides a comprehensive survey of the modeling 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 a unique text in the midst of many current books on chaos and complexity. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.

Product Details

ISBN-13:	9780198567905
Publisher:	Oxford University Press
Publication date:	08/04/2005
Pages:	408
Product dimensions:	9.30(w) x 6.20(h) x 1.00(d)

About the Author

Polytechnic of Turin

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