Book review

Although several hundreds books concerning chaotic dynamics have been already published, there are only few good books dealing with applications of chaos. I would mention the book M. Schroeder, Fractals, chaos, power laws, W.H. Freeman, 1991, as one of the best in this field. The present volume is another one.

The volume has resulted from the International Workshop on Applications of Chaos, held in San Francisco, December 1990, and contains 20 presentations of the workshop as well as many discussions. It covers diverse areas of applications from electrical engineering to medicine. One can see many well-known scientists, specifically P. Cvitanovic, J. Farmer, C. Grebogy, O. Rössler, J. Yorke, among the authors of the articles.

In many respects, the volume is not homogenous: included in it are: the articles of survey character as well as dealing with specific topics, the articles based on classical background as well as intended to open new areas. Also, the mathematical level of the articles is quite different. However there is one thing that is tying up all the articles, namely, all they concern applications of chaos. And this makes the volume good.

The articles, called chapters, are divided into five parts. First two parts, entitled Chaos in engineering and technological applications and Applications in physical sciences contain 12 articles. Three of them consider some general questions of analysis of chaotic systems and implications of chaos in engineering and technology. Another seven consider particular applications of chaos in different areas of mechanics and phisics, including atmospheric flight dynamics, convective flows, running belts, heat transfer, flame dynamics, coupled diods, dynamics of two connected electric generators. These ten articles have been written in a reasonably high level and consider the application fields that are presently quite standard. Two articles deal with applications in chemistry: one considers specific models of metal passivation and another article written by J.M. Ottino provides a well organized survey on applications of chaos in chemical engineering. This article is my favorite among the above mentioned twelve articles, may be, it is because I have learned quite a lot reading it.

Two not mathematical but still very interesting articles constitute the third part Applications in physiological sciences. Both concern the problem of chaotic dynamics in cardiology and provide examples of the principle that can be formulated as "decomplexification of disease". It means that normal, healthy dynamics appears to be the most chaotic but a disease typically leads to a reduction in apparent chaos.

The last two parts of articles, entitled Chaotic time series and forecasting and General topics contain three articles each. Their average mathematical level is a bit higher than of others but they do not deal so much with applications. These articles mainly concern with the mathematical phylosophy of chaos. It seems that three or four of them will have some influence on the whole subject of chaos and will be broadly cited. I especially want to mention the work Nonlinear modelling of chaotic time series: Theory and application authored by a group of scientists from the Los Alamos National Laboratory and devoted to recent developments in modelling and prediction of nonlinear time series.

Certainly, it is not possible to touch all applications of chaotic dynamics in one, even big, volume. But the present one touches quite many areas of application. As a whole, the volume provides a good demonstration of the interdisciplinary nature of chaos as well as of importance of the chaotic dynamics study in many areas of applied science and technology.

In general, the volume looks very attractive in many respects including the high level and beauty of presentation in most articles, the quality of publishing, broad range of questions under discussion. It is definitely a worthwile addition to the existing literature on chaos. The book is addressed to physicists, chemists, mathematicians, engineers, physiologists and specialists in other fields connected with either the theory of chaos or applications of chaotic dynamics. And it is very likely that all or almost all of them would be able to find something of specific interest in the volume.

The book is not expensive relative to its contents. Its purchase might be a very good investment for scientists of various specialities dealing with both theory and applications of chaotic dynamics. Purchase of the book is especially recommended to the libraries of the institutions where applications of chaos are among the topics of research.