UK Nonlinear News, May 2003

Nonlinear Dynamics and Chaos: Where do we go from here?

John Hogan, Alan Champneys, Bernd Krauskopf, Mario di Bernardo, Eddie Wilson, Hinke Osinga, and Martin Homer (editors)

Reviewed by by Jean-Luc Thiffeault

Institute of Physics, 2003, 358 pages.
Hardback, 40.00
ISBN: 0-7503-0862-1

This handsome volume is the proceedings of a conference held in Bristol in 2001, which had the aim of charting new directions for the exploration of nonlinear dynamical systems. This is a welcome endeavour: the field having matured as much as it has in the past thirty-odd years, it can be difficult for a curious student to gain a sense of what types of problems are being tackled, and where important challenges for the future lie.

The organisers have wisely chosen a relatively small number of contributors and given them considerable leeway to expound on their topic, with article lengths ranging from twenty to forty pages. Of course, such an ambitious programme cannot possibly cover every area of modern nonlinear dynamics, so the central, unifying themes of the meeting were chosen to be neural and biological systems, spatially extended systems, and experimentation in the physical sciences. This seems to me to strike the right balance between generality on the one hand, and not excessively diluting the goal of the conference on the other.

The contributing authors are leaders in their respective fields. The selection of topics includes multiple time scale dynamical systems (Guckenheimer), many-body quantum mechanics (MacKay), hereditary dynamical systems (van der Heiden), stability of optical pulses (Jones), spatio-temporal communication (Van Wiggeren, Garcia-Ojalvo, and Roy), pattern formation (Knobloch; Ermentrout and Osan), experimental fluid dynamics (Mullin), time-reversed acoustics (Fink), non-locally-coupled oscillators (Kuramoto), vortex dynamics in nonlinear media (Winfree), pattern formation in the visual cortex (Bressloff and Cowan), and spatio-temporal nonlinear dynamics (Ditto).

The editors must be commended for their work: the individual chapters have been given a clean, uniform style that reflects a serious effort to present the volume as a unified book rather than a collection of articles, with several cross-references between the chapters. The book is also remarkably free of typographical errors.

The best of the articles preserve the informal air of a speculative conference, and for the most part present a nice balance of material that escalates in difficulty. For instance, in his article on on many-body quantum mechanics, Robert MacKay first gives his "take" on quantum mechanics and how it relates to classical mechanics, and explodes the myth that quantum mechanics, being linear, cannot exhibit chaos. (His argument: classical Hamiltonian mechanics, expressed in Poisson bracket form, also appears linear over functionals! And yet...) He then formulates a series of guiding questions to orient the reader, gives speculative answers to them, and then spends the remainder of the article tackling more specific problems for many-body quantum mechanics. It makes for nice reading, as do the other articles in the collection.

I heartily recommend this collection to students looking for some direction (as long as they don't think this is all of nonlinear dynamics!), in spite of the fact that some articles are considerably more technical than others. Researchers who want to know the state of affairs in some promising areas will also find much to ponder therein.

UK Nonlinear News thanks the Institute of Physics for providing the review copy.

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Last Updated: 13th May 2003.