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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010105523 | Q172.5.C45 B47 2005 | Open Access Book | Book | Searching... |
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Summary
Summary
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.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 of complexity: 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.
Author Notes
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.
Reviews 1
Choice Review
Bertuglia and Vaio (both, Polytechnic of Turin, Italy), in their book's first part, "Linear and Nonlinear Processes," begin with a detailed discussion of mathematical modeling in its historical context, often touching on its philosophical ramifications. The limitations of linear models are clearly exemplified as are the difficulties inherent in nonlinear models. Of particular interest and value are the extensions of the concepts and models to economics and to social processes. The case of two interacting populations is followed from the linear model to the Volterra-Lotka model and its variants, and modified to study population-income models of some major US cities. In part 2, "From Nonlinearity to Chaos," the authors present a broader and more analytical study than is usual for this topic. From the question of the stability of the solar system to determinism in economics and spatial interaction models, they cover a wide range of chaos theory without omitting the basics of attractors, Lyapunov exponents, and other concepts. Compared to these parts, the last one, "Complexity," is a disappointment. It is repetitive, at times plodding, and by itself shows that complexity theory is still in its infancy. Extensive bibliography; subject and name indexes. A refreshingly new approach to the subjects. ^BSumming Up: Recommended. Upper-division undergraduates through professionals. J. Mayer emeritus, Lebanon Valley College
Table of 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 |
