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 text in
the midst of many current books on chaos and complexity.
Contents
Preface
Part I: Linear and nonlinear processes
1.1. Introduction
1.2. Modelling
1.3. The Origins of System Dynamics: Mechanics
1.4. Linearity in Models
1.5. One of The Most Basic Natural Systems: The Pendulum
1.6. Linearity as a First,
Often Insufficient Approximation
1.7. The Nonlinearity of Natural Processes: The Case of The Pendulum
1.8. Dynamical Systems and The Phase Space
1.9. Extension of The Concepts and Models Used in Physics to Economics
1.10. The Chaotic Pendulum
1.11. Linear Models in Social
Processes: The Case of Two Interacting Populations
1.12. Nonlinear Models in Social Processes: The Model of Volterra-Lotka and Some of Its Variants in Ecology
1.13. Nonlinear Models in Social Processes: The Volterra-Lotka Model Applied to Urban and Regional Science
Part II: From
nonlinearity to chaos
2.1. Introduction
2.2. Dynamical Systems and Chaos
2.3. Strange and Chaotic Attractors
2.4. Chaos in Real Systems and in Mathematical Models
2.5. Stability in Dynamical Systems
2.6. The Problem of Measuring Chaos in Real Systems
2.7. Logistic
Growth as A Population Development Model
2.8. A Nonlinear Discrete Model: The Logistic Map
2.9. The Logistic Map: Some Results of Numerical Simulations and An Application
2.10. Chaos in Systems: The Main Concepts
Part III: Complexity
3.1. Introduction
3.2. Inadequacy
of Reductionism
3.3. Some Aspects of The Classical Vision of Science
3.4. From Determinism to Complexity: Self-Organisation, A New Understanding of System Dynamics
3.5. What is Complexity?
3.6. Complexity and Evolution
3.7. Complexity in Economic Processes
3.8. Some Thoughts
on The Meaning of 'Doing Mathematics'
3.9. Digression into The Main Interpretations of The Foundations of Mathematics
3.10. The Need for A Mathematics of (or for) Complexity
References
Name Index
Subject Index
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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.
