This book is a follow-up to "Dynamical Systems with Applications
using Maple" by the same author. It covers the same topics, which
range from simple discrete dynamical systems, like the tent map, to
more advanced systems like linear and nonlinear differential
equations, Poincaré maps, local and global bifurcations, neural
networks and Hilbert's 16th problem.
The different chapters start with
an introduction to the topic and give a list of
references. Furthermore, they contain a section with short MATLAB
routines, which show possible treatments of the simple typical
examples by MATLAB methods.
Unfortunately, the treatment of the major part of the
material is quite cursory. For most dynamical systems only
bifurcation diagrams from simple simulations or phase portraits are
displayed.
Especially in the chapter about local bifurcation theory I
would expect some hints about center manifolds or Normal Form
Theory. Also the Hopf bifurcation is stated in its simplest form. The
author should definitively show some real world problem which bifurcates to
periodic solutions. The pitchfork diagrams in Chapter 12 (e.g. Figures
12.2, 12.6, 12.8) are also a nuisance because they show a sharp
corner at the bifurcation point where the bifurcating branch has a
vertical tangent. Since at the end of the chapter there is a small
MATLAB function which draws these diagrams, the author should have
noticed the difference. There should also be some hint to the Matcont
program which treats bifurcation problems very comfortably, or to any
other software package for this kind of problems.
My second criticism concerns the MATLAB part. Since MATLAB is directed
more towards numerical calculations, while Maple's main strength are
symbolic calculations, I would have hoped that the
numerical aspects and possibilities are treated more intensively. I
would also really have liked a closer connection between the main text and
the program examples. There could be some section in each chapter, where
the author elaborates how MATLAB could be used to treat the problems
at hand. Also, the worked out programs at the end are quite simple and
do not give a proper impression of MATLAB's capabilities. There are also
almost no comments, which is reasonable for these problems, but the
educational value would be significantly larger if the treatment of
harder problems would be demonstrated by well-documented code snippets.
The main merits of the book are the well understandable introduction to
different topics in dynamical systems and the presentation of quite a
large number of applications, together with a well selected
bibliography.