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Published in 1995 by Sage Publications (Thousand Oaks, CA) as Volume 107 in the Quantitative Applications in the Social Sciences series.

Chaos and Catastrophe Theories

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From the publisher's description of the book:

Chaos and catastrophe theories have become one of the major frontiers in the social sciences. Brown helps to clarify this complex new technique for modeling by approaching it with the following questions: What is Chaos? How can it be measured? How are the models estimated? What is catastrophe? How is it modeled? Beginning with an explanation of the differences between deterministic and probabilistic models, Brown introduces the reader to chaotic dynamics. Other topics covered are finding settings in which chaos can be measured, estimating chaos using nonlinear least squares, and specifying catastrophe models. Finally, the author estimates a nonlinear system of equations that models catastrophe using real survey data. Researchers wanting to understand and make use of this exciting new direction in social measurement and modeling will find this book an excellent and cogent introduction.

Table of Contents

  1. Working with Deterministic Mathematical Models
    The Argument in Favor of the Deterministic Approach
  2. What is Chaos?
    Necessary Conditions for Chaos
    Characteristics of Chaos
  3. Measuring Chaos
    Lyapunov Characteristic Exponents
    Fourier Analysis
    Phase Space Reconstruction of an Attractor Using Data
    The Spatial Correlation Test
  4. Estimating Chaos Models
    The Problem of Step Size
    Comparing the Model's Predicted Values to the Data
    The Future of Chaotic Studies in the Social Sciences
    An Alternative Approach for Maps
  5. What is Catastrophe?
    Placing the Cusp in the Range of the Data
  6. Strategies for Specifying Catastrophe Models
  7. Estimating Catastrophe Models
    References