UK Nonlinear News, August 1999


From Chaos to Order: Methodologies, Perspectives and Applications

By G. Chen and X. Dong

Reviewed by Thomas Schreiber

World Scientific Series on Nonlinear Science - Series A Vol. 24 (1998)
760pp, 312 Figs, and 728 Refs, $88.
World Scientific Pub. Co., Singapore. May 1998.
ISBN 981-02-2569-5

The publisher's announcement of this volume was published in Issue 16


As you may have guessed from the title, this is a book on the control of chaos. That the seemingly undesired instability of nonlinear systems can be turned into a virtue by exploiting it to make such systems highly controllable has boosted interest in nonlinear dynamical science. This perspective dates back to the famous Ott-Grebogi-Yorke paper [1]. Two of the few protagonists of the movement with strong backgrounds in both nonlinear dynamics and in classical control theory are Guanrong Chen and Xiaoning Dong. It is very fortunate that these two have opened their treasure chest to the public in an impressive volume covering an enormous range of aspects of chaos control.

After a brief but to-the-point introduction to dynamical systems and chaos, they present material on both open loop and closed loop strategies, parametric and feedback control, engineering aspects, synchronization, communication, distributed systems, anti-control, just to mention a few. The wide coverage of their 700 plus pages is reflected in the 700 plus references given. Thus, the immediate merit of the volume is to spare you the trouble of going through 700 research articles by offering 700 pages of contiguous text. The authors have mastered this difficult task in information compression with a minimal rate of loss, resulting in a rather dense but still quite readable text.

As a comprehensive representation of the state of the field of chaotic control this book will be hard to beat. Anybody who plans to apply control to an unstable system will start well prepared after going through Chen and Dong's opus. Still, I haven't given up the hope that someone will complement this publication by one that is maybe less complete, maybe less faithful to the original literature, but more digestible, more unified, more structured. Are all these approaches really different? Which differences are essential or paradigmatic, which are merely cosmetic or just rooted in the different traditions of the authors? Which methods are not-to-be-without, which ones are rather specialised and only useful in specific contexts? Maybe it is too much to ask to have a book of 300 pages or so after reading which I would know what chaos control is really all about and what it is good for. I personally would need such a book to prepare myself for Chen and Dong's.

The hardcover, considering its size, is not overpriced at US $88. The production quality, however, is less then superb. Most of the resolution available in book production is wasted, probably by using camera-ready laser prints provided by the authors. The figures are often rather poor-quality reproductions from other publications, featuring broken lines and unreadable lettering.

In summary, anyone interested in controlling nonlinear systems should have a copy of this outstanding volume on their shelves. But somebody should write that other book.

References

  1. E. Ott, C. Grebogi, and J.A. Yorke. Controlling chaos. Phys. Rev. Lett., 64, 1196, 1990.

UK Nonlinear News thanks World Scientific for providing a copy of this book for review.


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