Chaotic Systems

2011·27.2 MB·English

by  Esteban Tlelo-Cuaulte

CHAOTIC SYSTEMS
Edited by Esteban Tlelo-Cuautle
Chaotic Systems
Edited by Esteban Tlelo-Cuautle
Published by InTech
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Copyright © 2011 InTech
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First published February, 2011
Printed in India
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Additional hard copies can be obtained from [email protected]
Chaotic Systems, Edited by Esteban Tlelo-Cuautle
p. cm.
ISBN 978-953-307-564-8
free online editions of InTech
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Contents
Preface IX
Part 1 Chaotic Systems 1
Chapter 1 Short-Term Chaotic Time Series Forecast 3
Jiin-Po Yeh
Chapter 2 Predicting Chaos with Lyapunov Exponents:
Zero Plays no Role in Forecasting Chaotic Systems 25
Dominique Guégan and Justin Leroux
Chapter 3 Relationship between the Predictability Limit
and Initial Error in Chaotic Systems 39
Jianping Li and Ruiqiang Ding
Chapter 4 Microscopic Theory of Transport Phenomenon
in Hamiltonian Chaotic Systems 51
Shiwei Yan
Part 2 Chaos Control 117
Chapter 5 Chaos Analysis and Control
in AFM and MEMS Resonators 119
Amir Hossein Davaie-Markazi and Hossein Sohanian-Haghighi
Chapter 6 Control and Identification of Chaotic Systems
by Altering the Oscillation Energy 135
Valery Tereshko
Chapter 7 Adaptive Control of Chaos 161
Hassan Salarieh and Mohammad Shahrokhi
Part 3 Synchronization 185
Chapter 8 Chaotic Clustering: Fragmentary
Synchronization of Fractal Waves 187
Elena N. Benderskaya and Sofya V. Zhukova
VI Contents
Chapter 9 Coexistence of Synchronization and Anti-Synchronization
for Chaotic Systems via Feedback Control 203
Hammami Sonia and Benrejeb Mohamed
Part 4 Applications 225
Chapter 10 Design and Applications
of Continuous-Time Chaos Generators 227
Carlos Sánchez-López, JesusManuel Muñoz-Pacheco, Victor Hugo
Carbajal-Gómez, Rodolfo Trejo-Guerra, Cristopher Ramírez-Soto,
Oscar S. Echeverria-Solis and Esteban Tlelo-Cuautle
Chapter 11 Applying Estimation Techniques
to Chaos-based Digital Communications 255
Marcio Eisencraft and Luiz Antonio Baccalá
Chapter 12 Emergence of Matured Chaos During, Network Growth,
Place for Adaptive Evolution and More of Equally Probable
Signal Variants as an Alternative to Bias p 281
Andrzej Gecow

Preface
This book represents a collection of major developments in the area of Chaotic Systems.
Researchers from around the world summarize key guidelines on modeling, simula-
tion, control synchronization, and applications of these systems. The organization of
the book includes twelve chapters covering a wide variety of engineering areas regard-
ing basic scientifi c research and technological development.
The fi rst chapter presents a time series technique to forecast future events. The sec-
ond chapter analyzes forecasting chaos, providing a deep insight on the meaning of
Lyapunov exponents locally. The predictability of chaotic events considering initial
error in chaotic systems is presented in chapter three. The fourth chapter introduces a
microscopic theory of transport phenomena which is supported by applying Hamilto-
nian forms. These four chapters motivate the reader to look for approaches to control
and synchronization of chaotic systems. Furthermore, chapters fi ve, six and seven
focus on controlling the chaos phenomenon. For instance, micro-electromechanical
systems like resonators might present chaotic behavior, the prediction and control of
chaos is then presented in chapter fi ve. Chaotic systems can be perturbed, and control
and identifi cation approaches can be applied as shown in chapter six. Among all tech-
niques for controlling chaos the adaptive one is very useful, as described in chapter
seven. Chaos systems can be synchronized as shown in chapters eight and nine. In
chapter nine a technique for chaos control called feedback control, is also presented.
Some realizations of chaotic oscillators with electronic circuits are presented in chap-
ter ten. In this chapter two chaos systems are synchronized by Hamiltonian forms
and observer approach, to realize a secure communication system. Chapter eleven
introduces estimation techniques for chaos systems to develop digital communica-
tions. Some open research problems can be identifi ed in these eleven chapters, as well
as in the fi nal chapter devoted to the emergence of matured chaos during network
growth.
This book includes recent advances in science and engineering applications. However,
as highlighted in the majority of chapters, still many research and applications are
very much in need of further development. In this way, the book is a good source for
identifying basics on chaotic systems, techniques to control and synchronize them,
and to acquire recent knowledge and ideas for future research in this area. Some ap-
plications to engineering motivate the reader to develop experiments applied to real
X Preface
life problems. This book is intended for students, academia and industry since the col-
lected chapters provide a rich cocktail while balancing theory and applications.
Enjoy the book!
Esteban Tlelo-Cuautle
INAOE
Department of Electronics
Mexico