UK Nonlinear News, November 1999

CHAOS for Engineers: Theory, Applications, and Control

By T. Kapitaniak

Reviewed by Thomas Schreiber

Springer-Verlag Berlin Heidelberg (1998)

When reading this book I realised that, despite its many precedents, it fills a gap. I don't know any other text that offers a comparably hand-picked selection of material on chaos, being at the same time accessible to an engineering student and mathematically precise.

The rather slim volume (150 pages) is aimed at, say, a graduate student in engineering. It can thus assume a higher command of mathematical techniques than, for example, Understanding Nonlinear Dynamics by Kaplan and Glass (Springer-Verlag 1995) which is primarily written with students in the biological sciences in mind. On the other hand, other texts at a comparable mathematical level are invariably more voluminous, either because they serve the double purpose of an introduction and a reference text, or because they add extensive case studies of applications, often in a more qualitative style.

You will learn the basics of dynamicals systems (continuous and discrete), attractors, invariants, bifurcations, fractals, intermittency. Finally there are a few real examples and a chapter on chaos control. The theoretical sections are augmented by instructive exercises. Of course, Kapitaniak's book does not claim to present all of chaos theory. Nor will you find a host of "success stories" told to convince you that this is an important subject. But everything that is covered is crystal clear, readily understandable and highly dependable concerning the factual content. The language is straight - you are told all you need to know without being drowned in words. Mathematical language is used very efficiently. Notation is not introduced for its own sake but to accompany the analytic argument and to enable a high degree of preciseness.

After reading about the new ideas in nonlinear dynamics presented here, the engineer will find that there is still a long way to go before she or he can apply these ideas to real world problems - few engineers are getting paid for controlling Chua's circuit. Nevertheless, the reader will appreciate the appeal of recent nonlinear dynamics. They will find Chaos to be not just one more fashionable gimmick but rather something that is interesting, understandable, and potentially very useful.

CHAOS for Engineers is a highly recommendable book. It offers one of the most efficient entry points to chaos theory I know of, given a mathematical background typical for engineering and science students.

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