Elegant Chaos

by Julien Clinton Sprott

This heavily illustrated book collects in one source most of the mathematically simple systems of differential equations whose solutions are chaotic. It includes the historically important systems of van der Pol, Duffing, Ueda, Lorenz, Rössler, and many others, but it goes on to show that there are many other systems that are simpler and more elegant. Many of these systems have been only recently discovered and are not widely known. Most cases include plots of the attractor and calculations of the spectra of Lyapunov exponents. Some important cases include graphs showing the route to chaos. The book includes many cases not previously published as well as examples of simple electronic circuits that exhibit chaos. No existing book thus far focuses on mathematically elegant chaotic systems. This book should therefore be of interest to chaos researchers looking for simple systems to use in their studies, to instructors who want examples to teach and motivate students, and to students doing independent study.

302 pages, Paperback

First published March 22, 2010

Reviews

[Robert · Rating 5 out of 5]

Well, this was a quiet delight. It isn't a good introduction to anything, but then, it isn't intended to be, either. If you haven't already read a text on dynamical systems theory and (probably less crucially) one on non-linear time series analysis, a lot of this will be fairly opaque. If you aren't familiar with differential equations, you have very little hope indeed. But if you do have the appropriate background, this is a great trove of examples of relatively simple chaotic dynamical systems, with many illustrations, thus acheiving its actual aim. There were several nuggets of new (to me) knowledge and acknowledgement of the limits of anyone's knowledge, useful for researchers - though it was published in 2010 and no doubt matters have moved on along many fronts since then. I wish I'd come across this several years ago - would have helped me no end with certain research problems.