I only write this review to repudiate a previous reviewer's comment that this is a good book on "chaos". No, it is not. There is no detailed 'first-principles' description of ANYTHING that forms the theoretical basis of deterministic dynamical systems. So, don't buy this book for a first-glance at analysis of dynamics in chaotic systems! (Typically, I assume, one needs to understand the theory before attempting to decipher experiments. Try the books by
Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in nonlinearity)
Strogatz or
Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists
Thompson-Stewart or
Chaos
Tsonis, for a structured forage into theoretical chaos)
What this book is, is a review/collection of revised manuscripts of some fine articles published by the authors and others who were looking to quantify the experimentally-observed dynamics of chaotic systems. The first edition (1999) of this book is more of a collection of notes, but the second edition is far more comprehensive and well-structured.
The target audience for this book are advanced graduate students who are acquainted with the theory governing nonlinear dynamical systems, undergrad-level stats and advanced linear algebra (topics in topology?). (This 'target audience' description is not didactic as I myself did (do) not know much about either topology or stats before working with this book.)
As the analysis of any experiment is truly just an exercise in statistics, this book expects a broad familiarity with statistical methods. This book is not a general collection of tools that can be applied to every signal out there. So it is expected that the reader already possesses a highly nonlinear/weakly stationary signal that they are interested in deciphering. The authors also provide an online repository of some data sets and routines used as examples in the book (TISEAN package?).
This book steps the reader through specific flavors of embedding, false neighbors counting, linear and nonlinear forecasting techniques through the chapters. In spite of that, most chapters can be used as stand-alone monographs with few continuity issues.
I find the references at the end of each chapter to be sufficient.
Over all, I find this book extremely useful and I have both the two editions in my library. Like most books however a negative feature of this book is that it takes its time in getting to the point (which sometimes gets spread between chapters). I found reading the original articles, cited in a section, before reading that section in the book itself to be particularly helpful.
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