The Illustrated Dictionary of Nonlinear Dynamics and Chaos

T. Kapitaniak and S.R. Bishop

Reviewed by Ulrike Feudel

Hardcover - 280 pages (January 1999)
John Wiley and Sons ISBN: 0471983233
75.00

The study of nonlinear dynamical systems is a quickly developing field of research in modern science. Starting from pioneering works in pure and applied mathematics, it is now of great impact on many disciplines in natural sciences like physics, chemistry, biology and engineering but also in social sciences like economy. This diversity of applications requires books which explain the basic mathematical concepts in a rather simple way using examples for illustration. The Illustrated Dictionary of Nonlinear Dynamics and Chaos follows this idea. It provides an explanation for many terms from the vocabulary used in textbooks on nonlinear dynamics as well as in original papers. The alphabetic order enables the reader for a quick search. Even when alternative terms are used in literature for the same subject, cross-references help to find the right entry. The dictionary contains not only the mathematical concepts but also terms from various, frequently discussed applications. This makes the dictionary to a helpful source of information for everybody interested in nonlinear science. Moreover, the majority of the most studied model equations and maps like the Lorenz system, the Duffing oscillator, the logistic and circle maps are presented. I like very much the excellent illustrations for many ideas in nonlinear dynamics, but unfortunately, a few of the pictures of beautiful attractors like the double scroll attractor are of poor quality.

This dictionary is highly valuable for researchers dealing with nonlinear problems, who want to find a quick answer on several questions. Since the entries are often formulated using a mathematical oriented language, some backround in mathematics is needed for understanding. On the other hand, if the reader is interested in more details, he can look into the references in the large bibliography. This is especially recommended for newcomers in the field, who might need a textbook for further reading. The comprehensive bibliography contains only a few original papers. The majority of references are textbooks on various subjects of nonlinear dynamics or related topics. In particular, students will benefit from this collection of books to choose from for further studies.

Nowadays nonlinear dynamics is a widely developed field which makes it extremely difficult to give a complete description of all terms used. Therefore, the authors restrict themselves to temporal evolution equations (ordinary differential equations) and maps. Pattern formation in spatio-temporal systems is beyond the scope of this dictionary. Also nonlinear time series analysis, another big part of nonlinear dynamics, is reduced to a few entries. Nevertheless, the authors did an important and very valuable job in compiling this dictionary which will be of great help for students as well as for researchers in saving time to get aquainted with the concepts of nonlinear dynamics.

UK Nonlinear News thanks John Wiley and Sons for providing a copy of this book for review.


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