The Synchronized Dynamics of Complex Systems, Volume 6

1st Edition

Series Editors: Albert Luo George Zaslavsky
Authors: Stefano Boccaletti
Hardcover ISBN: 9780444527431
eBook ISBN: 9780080560427
Imprint: Elsevier Science
Published Date: 5th February 2008
Page Count: 258
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Table of Contents

Chapter 1 – Preface Chapter 2 – Introduction Chapter 3 – Identical Systems Chapter 4 – Non identical Systems Chapter 5 – Structurally non equivalent Systems Chapter 6 – Effects of noise Chapter 7 – Distributed and Extended Systems Chapter 8 – Complex Networks


The origin of the word synchronization is a greek root, meaning "to share the common time". The original meaning of synchronization has been maintained up to now in the colloquial use of this word, as agreement or correlation in time of different processes. Historically, the analysis of synchronization phenomena in the evolution of dynamical systems has been a subject of active investigation since the earlier days of physics.

Recently, the search for synchronization has moved to chaotic systems. In this latter framework, the appearance of collective (synchronized) dynamics is, in general, not trivial. Indeed, a dynamical system is called chaotic whenever its evolution sensitively depends on the initial conditions. The above said implies that two trajectories emerging from two different closeby initial conditions separate exponentially in the course of the time. As a result, chaotic systems intrinsically defy synchronization, because even two identical systems starting from slightly different initial conditions would evolve in time in a unsynchronized manner (the differences in the systems' states would grow exponentially). This is a relevant practical problem, insofar as experimental initial conditions are never known perfectly. The setting of some collective (synchronized) behavior in coupled chaotic systems has therefore a great importance and interest.

The subject of the present book is to summarize the recent discoveries involving the study of synchronization in coupled chaotic systems. Not always the word synchronization is taken as having the same colloquial meaning, and one needs to specify what synchrony means in all particular contexts in which we will describe its emergence.

The book describes the complete synchronization phenomenon, both for low and for high dimensional situations, and illustrates possible applications in the field of communicating with chaos.

Key Features

· Technical, but not specialistic language · About 100 illustrative Figures · Full overview on synchronization phenomena · Review of the main tools and techniques used in the field · Paradigmatic examples and experiments illustrating the basic concepts · Full Reference to the main publications existing in the literature on the subject


Senior graduate students, Established researchers in the area


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© Elsevier Science 2008
Elsevier Science
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About the Series Editors

Albert Luo Series Editor

Albert C.J. Luo received his B.S. in Mechanical Engineering (1984) and M.S. in Engineering Mechanics (1990) in China and Ph.D. in Applied Mechanics (1996) in Canada. During 1996-1998, he was an NSERC (Canada) post-doctoral fellow at UC Berkeley. From 1998-present, Dr. Luo have worked at Southern Illinois University Edwardsville as Assistant/Associate Professor. During 20 year research experience, Dr. Luo developed stochastic and resonant layer theories in nonlinear Hamiltonian systems; a local theory for non-smooth dynamical systems on connectable domains. In addition, Dr, Luo also developed an approximate plate theory; a large damage theory for anisotropic materials and a generalized fractal theory. He has published over 130 peer-reviewed journal and conference papers. Dr. Luo has served editors for the Journal “Communications in Nonlinear Science and Numerical simulation” and two book series on Nonlinear Science and Complexity. Dr. Luo is the editorial member for IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control. He also organized over 10 international symposiums and conferences on Dynamics and Control.

Affiliations and Expertise

Southern Illinois University, Department of Mechanical and Industrial Engineering, Edwardsville, USA

George Zaslavsky Series Editor

Affiliations and Expertise

New York University, Courant Institute of Mathematical Sciences and Department of Physics, USA

About the Authors

Stefano Boccaletti Author

Affiliations and Expertise

CNR-Istituto dei Sistemi Complessi, Sesto Fiorentino, Florence, Italy