Controlling Chaos .. Theoretical, Practical Methods in Nonlinear Dynamics - Tomasz Kapitaniak - ( Academic Press, Elsevier - 1996 - pp.165 ).pdf

Preface
More than two decades of intensive studies on nonlinear dynamics have
posed the question on the practical applications of chaos. One of the possible
answers is to control chaotic behavior in such a way as to make it predictable.
Indeed, nowadays the idea of controlling chaos, which we try to explain in
this book, is an appealing one.
This book anized as follows. In Part I (Chapters 1-5) we describe
basic methods of controlling chaos, while in Part II we reprint fundamental
contributions to this field.
In Chapter 1 we give basic information about controlling procedures. Ideas
of feedback and nonfeedback methods as well as of chaos synchronization
are explained. Additionally, we describe Chua's circuit (a very simple
electronic device) which will be used in several examples in the following
chapters.
Chapter 2 describes feedback controlling methods in which unstable
periodic orbits embedded in the chaotic attractor are stabilized. We discuss
the Ott-Grebogi-Yorke and Pyragas methods and their connections with
classical controlling methods. The method of controlling chaos by chaos, in
which chaotic behavior can be modified by coupling via a feedback loop with
another chaotic system, is also mentioned.
Nonfeedback methods are explained in Chapter 3. This approach is
inevitably much less flexible than feedback methods, but in many practical
systems it is easier to apply. We give methods in which chaos can be
controlled through operating conditions or by system design. Additionally,
taming chaos, entrainment and migration control procedures are discussed.
The synchronization chaos procedures of Chapter 4 allow two chaotic
systems to have exactly the same response. The procedures of Pecora and
Carroll and of continuous control are described. We also explain the idea of
munication.
In Chapter 5 we discuss the problem of the selection and engineering
implementation of the chaos controlling method for a