UK Nonlinear News, August 2002
Scator Verlag Publishers, 2001
This is a good introductory text at the graduate level (or possibly for some advanced and/or enthusiastic undergraduates). Schuster writes well and makes a good selection of modern ideas, weaving a complex pattern of inter-related subjects which are all connected by their ability to display fascinating behaviour, especially when a feedback mechanism exists. Hence, it is a great shame that the production quality of this book is not of the same high standard as his well-known book "Deterministic Chaos", or competitors texts such as "Critical Phenomena in Natural Sciences", by Didier Sornette. (Actually, I originally planned to make detailed comparisons with this latter named book, but while they are both marvellous modern texts on complex systems, there is really only a minimal overlap in topics.)
The material is arranged into seven main chunks, beginning with an introduction. Second is a "concepts" chapter, which provides necessary elementary material on dynamical systems, populations, complexity, cellular automata and control systems. Third is evolution and computation, where Schuster really begins to show how computational systems can be constructed in such a way that their behaviour "mimics Darwinian evolution". Fourth is neural networks, which is discussed as presenting another universal model for complex adaptive systems, albeit with a variety of learning strategies from which to choose, and is linked to observations on activities such as speech in the human brain. Fifth is games, self-organised criticality and co-evolution, where Schuster considers some of the classic examples (such as Bak's sandpile model) and then uses a fitness criteria to introduce randomness into the system in a way that might be a reasonable model for mutating species. Sixth is a summary and outlook. Finally, there is a seventh chapter, which is really a very useful appendix, introducing excellent material on stochastic processes, chaos, automata, the Ising model and Lyapunov functions. In fact, this chapter is material with which Schuster is clearly very much at home and is a real highlight of the book. There are a small number of exercises (and solutions) at the end of most of the chapters, and these are there to tease out extra interesting topics rather than to really give homework exercises for the students.
In summary, this is a fantastic sourcebook of topics old and modern which are all relevant to our understanding of how to mathematically construct and analyse complex systems which possess the ability to be adaptive, although I would expect many readers to become a little frustrated with some of the typographical errors and also a little bewildered by the multitude of topics that are woven into the tapestry of this useful, new book. My one persistent philosophical problem with the links to real systems that are made by Schuster (and many others), are the extent to which we can verify that a mechanism in a mathematical or computational model mirrors an actual biological, chemical or physical mechanism, even when the model displays life-like behaviour.
UK Nonlinear News thanks Professor H.G. Schuster for providing a review copy of this book.
A listing of books reviewed in UK Nonlinear News is available.