UK Nonlinear News, August 2002


Nonlinear Dynamics and Chaos (2nd edition)

J.M.T. Thompson and H.B. Stewart

Reviewed by John Hogan

Wiley. February 2002
ISBN: 0-471-87684-4.

Here is a prediction about this book. You will probably not buy it. But I think that it is very good and you should recommend it. Let me explain.

Back in July 1986, the nuclear power station at Chernobyl had already exploded covering lots of Europe in radioactive material. Madonna was top of the charts with "Papa don't preach" and Nick Kamen had just taken off his Levi jeans in that launderette, starting a whole new craze in boxer shorts.

At the same time, I was looking for some textbook that could explain, in a helpful way, everything I needed to know about Nonlinear Dynamics and Chaos. All three volumes of Abraham and Shaw had already appeared and they were pretty good on the pictures, but that excellence only emphasised what was missing. There was still no Moon or Guckenheimer & amp; Holmes to get my teeth into.

Then the first edition of "Thompson & Stewart" appeared (as all good books, it immediately became known by its authors names, rather than its title) and my career has never been the same since. It is hard to convey to younger readers just how influential that first edition became (for example, it never went out of print). Here was a book that brought together everything you needed to know to introduce you to the subject, whatever your background, was easy to read and had dozens of fantastic pictures which on their own were more than worth the cover price. In short, it inspired, as few books can ever claim to do.

OK now fast forward to 2002. Look on www.amazon.com and there are over 60 books on sale with Nonlinear Dynamics and Chaos in the title (including such exotic examples as "Nonlinear dynamics and chaos in agricultural systems", "Chaos, catastrophes & human affairs: applications of nonlinear dynamics to work, organisation and social evolution" and even "Clinical chaos. A therapists guide to nonlinear dynamics and therapeutic change"). Now compare the best of the rest with the 1986 Thompson & Stewart. Would you still recommend it to anyone? To be honest, I would not do so, not because of any fault in the book, but because the field has simply changed beyond recognition since then. What was ground-breaking in 1986 now looks very tired and dated (have you listened to that Madonna track recently?).

Well I guess Thompson & Stewart could both have said we did a great job in 1986, let's leave the field to others. On the other hand, doing nothing leaves their achievement looking tarnished to a younger audience.

What they and Wiley have decided to do is to produce an update of the material that is contained in the 1st edition. Out go the old chapters 16 & 17 (on particle accelerators and on the experimental observation of chaos respectively) and in comes a new chapter 16 on escape from a potential well. In too come a comprehensive illustrated glossary as well as a classification scheme of codimension 1 bifurcations. Lots of the text has been revised and all the pictures, including the 67 new ones, still glow, shine and inform as they did in 1986. There are also many new references (25 pages in all).

What they have not done is included anything significant on spatiotemporal systems, delays, piecewise systems, effects of noise, large dimensional systems or numerical continuation. The last area is a big omission in my view. AUTO appears not to deserve a single mention (in the glossary, appendix or references). It was certainly OK to omit it in 1986, just as the code was starting to become available but who now in the field is not affected by it?

What is missing is probably the reason why you, as a reader of UK Nonlinear News, will not be tempted to buy the book. You have already moved on. But what about those people outside the field? Would I recommend it to them? This time the answer is a definite yes. Certainly if an engineering colleague asks me for a book to read so that she can move into the field, I will immediately say "Thompson & Stewart, 2nd Edition". In other words, it is the community who do not read UK Nonlinear News who will decide the fate of this book. OK so you still can't use it as a book to lecture from and I doubt if it will have as much groundbreaking impact as the 1st Edition. But just as Madonna is still worth listening too, despite an overcrowded market full of wannabees, so too is Thompson & Stewart now restored to its rightful place as required reading if you want to know what all the fuss is about.

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

A listing of books reviewed in UK Nonlinear News is available.


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