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

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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.

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Product Details

  • ISBN-13: 9780198567912
  • Publisher: Oxford University Press, USA
  • Publication date: 7/1/2005
  • Pages: 404
  • Product dimensions: 9.10 (w) x 6.10 (h) x 1.00 (d)

Table of Contents

1 Introduction 3
2 Modelling 10
3 The origins of system dynamics : mechanics 19
4 Linearity in models 27
5 One of the most basic natural systems : the pendulum 32
6 Linearity as a first, often insufficient approximation 39
7 The nonlinearity of natural processes : the case of the pendulum 46
8 Dynamical systems and the phase space 49
9 Extension of the concepts and models used in physics to economics 60
10 The chaotic pendulum 67
11 Linear models in social processes : the case of two interacting populations 71
12 Nonlinear models in social processes : the model of Volterra-Lotka and some of its variants in ecology 93
13 Nonlinear models in social processes : the Volterra-Lotka model applied to urban and regional science 108
14 Introduction 125
15 Dynamical systems and chaos 127
16 Strange and chaotic attractors 141
17 Chaos in real systems and in mathematical models 154
18 Stability in dynamical systems 159
19 The problem of measuring chaos in real systems 179
20 Logistic growth as a population development model 190
21 A nonlinear discrete model : the logistic map 199
22 The logistic map : some results of numerical simulations and an application 214
23 Chaos in systems : the main concepts 231
24 Introduction 239
25 Inadequacy of reductionism 240
26 Some aspects of the classical vision of science 253
27 From determinism to complexity : self-organization, a new understanding of system dynamics 266
28 What is complexity? 275
29 Complexity and evolution 291
30 Complexity in economic processes 301
31 Some thoughts on the meaning of 'doing mathematics' 315
32 Digression into the main interpretations of the foundations of mathematics 329
33 The need for a mathematics of (or for) complexity 348
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