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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
- Working with Deterministic Mathematical Models
Argument in Favor of the Deterministic Approach
- What is Chaos?
Conditions for Chaos
- Measuring Chaos
Space Reconstruction of an Attractor Using Data
Spatial Correlation Test
- Estimating Chaos Models
Problem of Step Size
the Model's Predicted Values to the Data
Future of Chaotic Studies in the Social Sciences
Alternative Approach for Maps
- What is Catastrophe?
the Cusp in the Range of the Data
- Strategies for Specifying Catastrophe Models
- Estimating Catastrophe Models