This is the second edition of a nicely written and generously illustrated text introducing the reader to a wide variety of topics related to dynamics of complex dynamical systems. The principal differences to the previous edition consist in the inclusion of the new Chapter 3 that provides a brief introduction to information theory and statistics, followed by a discussion of the Shannon entropy, mutual information, and complexity measures. Several sections of the book have been revised and extended. The exercise sections have been expanded; solutions to the exercises that accompany Chapters 1‒8 are now collected in the final Chapter 9. The exposition is transparent and encyclopedically concise, each chapter contains information one needs in order to understand the main concepts, ideas and methods, but, as the author notices in the preface, “all of the chapters making this book deal with a subject worth devoting an entire course to”. The reader is supposed to have a basic knowledge of ordinary and partial differential equations, probability theory, and statistics. The book can be used both for self-study and as a reading for a course on complex systems; the choice of material is quite flexible due to the reduced dependence among the chapters, but this may also be viewed as a weak point, since the subject is highly interdisciplinary and there are interesting connections between the topics discussed in different chapters. The text should attract the attention of graduate students and scientists working in natural sciences, engineering, and neuroscience.
Reviewer: Yuri V. Rogovchenko (Umeå)