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Book review

Author(s) Neimark, Yu.I.
Landa, P.S.
Title Stochastic and Chaotic Oscillations
Publisher Kluwer Academic Publishers
Year of publication 1992
Reviewed by Viorica-Cerasela Postolache

Techniques involving the stochastic analysis find wide applications in many fields of science and engineering such that: mathematics, mechanics, chemistry, biology. The aim of this book is to present this important problem using computers science interrelations. This book is suitable for workers in all the fields presented above as well as for more advanced students in mathematics and computers.

The authors' aim have been to provide new results concerning backgrounds of stochastic analysis of some dynamical systems with examples drawn from various areas of applications. The range of topics covered is from simple mathematical models of some dynamical systems to advanced concepts such as order and chaos, stochasticity and bifurcation theory, attractors, quantitative characteristics of stochastic and chaotic motions. In this book can be found numerous examples of mechanical, physical, chemical and biological systems with chaotic and stochastic motions.

There exists a table of index and the table of contents is sufficiently detailed. Numerous pictures, carefully plotted, illustrate the ideas and the concepts. However the book is not so well produced. I shall give some examples:

a) the page 83 contains the name B. Rieman (!);

b) the page 324 contains "the word" computationof;

c) on the page 338, Fig. 9.41 is 9.40;

d) although the book includes a comprehensive bibliography this is not in alphabetical order;

e) the distance between rows is too much and consequently this lead to a growth of the book's price;

f) on the page 137 a.o. the symbol for the first derivative is difficult to read (more convenient is x' instead x'), and so on.

The reader should pay no attention to the graphical omissions of this edition.

Generally, the presentation is rigorous and reflects the experience of the two authors in the difficult field of dynamical systems and the computers research work. Since computers and dynamical systems are relevant in various life and social sciences, I expect that this book will be of interest to workers in these fields.

A knowledge of calculus and computers are assumed. However this book is sufficiently self contained to enable independent research. Consequently a large area of readers can use the book.