Nonlinearity, Chaos, and Complexity
The Dynamics of Natural and Social Systems
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Product details:
- Publisher OUP Oxford
- Date of Publication 12 May 2005
- ISBN 9780198567912
- Binding Paperback
- No. of pages404 pages
- Size 233x157x21 mm
- Weight 724 g
- Language English
- Illustrations numerous line drawings and mathematical examples 0
Categories
Short description:
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. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.
MoreLong description:
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.
...the book will certainly bring a lot of pleasure to the reader with philosophical inclinations
Table of Contents:
Contents
Preface
Part I: Linear and nonlinear processes
Introduction
Modelling
The Origins of System Dynamics: Mechanics
Linearity in Models
One of The Most Basic Natural Systems: The Pendulum
Linearity as a First, Often Insufficient Approximation
The Nonlinearity of Natural Processes: The Case of The Pendulum
Dynamical Systems and The Phase Space
Extension of The Concepts and Models Used in Physics to Economics
The Chaotic Pendulum
Linear Models in Social Processes: The Case of Two Interacting Populations
Nonlinear Models in Social Processes: The Model of Volterra-Lotka and Some of Its Variants in Ecology
Nonlinear Models in Social Processes: The Volterra-Lotka Model Applied to Urban and Regional Science
Part II: From nonlinearity to chaos
Introduction
Dynamical Systems and Chaos
Strange and Chaotic Attractors
Chaos in Real Systems and in Mathematical Models
Stability in Dynamical Systems
The Problem of Measuring Chaos in Real Systems
Logistic Growth as A Population Development Model
A Nonlinear Discrete Model: The Logistic Map
The Logistic Map: Some Results of Numerical Simulations and An Application
Chaos in Systems: The Main Concepts
Part III: Complexity
Introduction
Inadequacy of Reductionism
Some Aspects of The Classical Vision of Science
From Determinism to Complexity: Self-Organisation, A New Understanding of System Dynamics
What is Complexity?
Complexity and Evolution
Complexity in Economic Processes
Some Thoughts on The Meaning of 'Doing Mathematics'
Digression into The Main Interpretations of The Foundations of Mathematics
The Need for A Mathematics of (or for) Complexity
References
Name Index
Subject Index
