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The Synchronized Dynamics of Complex Systems, 6 : Volume 6 - Stefano Boccaletti

The Synchronized Dynamics of Complex Systems, 6

Volume 6


Published: 1st March 2008
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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.
Furthermore, the book summarizes the concepts of phase synchronization, lag synchronization, imperfect phase synchronization, and generalized synchronization, describing a general transition scenario between a hierarchy of different types of synchronization for chaotic oscillators.
These concepts are extended to the case of structurally different systems, of uncoupled systems subjected to a common external source, of space extended nonlinearly evolving fields, and of dynamical units networking via a complex wiring of connections, giving thus a summary of all possible situations that are encountered in real life and in technology.
-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

Prefacep. ix
Introductionp. 1
Identical Systemsp. 9
Complete synchronizationp. 9
The PC configurationp. 11
The APD configurationp. 14
Bidirectional coupling configurationsp. 15
The stability of the synchronized motionp. 17
The master stability functionp. 20
The case of time continuous systemsp. 20
The master stability function for coupled mapsp. 25
Assessing the synchronizabilityp. 25
Nonidentical Systemsp. 31
Phase synchronization of chaotic systemsp. 33
Synchronization of periodic oscillatorsp. 33
Phase of chaotic signalsp. 36
Phase entrainment of externally driven chaotic oscillatorsp. 41
Phase synchronization of coupled chaotic oscillatorsp. 45
Transition to phase synchronization of chaosp. 47
Experimental verification of the transition to phase synchronizationp. 49
Ring intermittency at the transition to phase synchronizationp. 53
Imperfect phase synchronizationp. 58
Lag synchronization of chaotic oscillatorsp. 61
Intermittent lag synchronizationp. 63
Phase synchronization of nonautonomous chaotic oscillatorsp. 69
Generalized synchronizationp. 74
A mathematical definition of synchronizationp. 78
Synchronization of structurally nonequivalent systemsp. 83
From chaotic to periodic synchronized statesp. 85
Systems with coexisting attractorsp. 88
Methods and tools for detecting synchronized statesp. 94
Detection of a functional relationshipp. 95
Embedding and multivariate datap. 96
Interdependence between signalsp. 98
Predictability of time seriesp. 99
Coupling directionp. 101
Detection of phase synchronizationp. 101
Detection of local synchronizationp. 104
Effects of Noisep. 111
Noise-induced complete synchronization of identical chaotic oscillatorsp. 112
Noise induced phase synchronization of nonidentical chaotic systemsp. 117
Noise enhanced phase synchronization in weakly coupled chaotic oscillatorsp. 120
Constructive noise effects in systems with noncoherent phase dynamicsp. 122
Noise-induced changes in time scale and coherence resonancep. 124
Noise-induced complete synchronizationp. 126
Noise-enhanced phase synchronization, deterministic and stochastic resonancep. 129
Distributed and Extended Systemsp. 135
Synchronization in a chain of coupled circle mapsp. 136
Phase synchronization phenomena in a chain of nonidentical phase coherent oscillatorsp. 140
Collective phase locked states in chains of phase coherent chaotic oscillatorsp. 142
In phase and anti-phase synchronization in chains of homoclinic oscillatorsp. 146
Synchronization domains and their competitionp. 151
Synchronization in continuous extended systemsp. 157
Asymmetric coupling effectsp. 164
Defect enhanced anomaly in asymmetrically coupled spatially extended systemsp. 173
Convective instabilities of synchronization in space distributed and extended systemsp. 178
Complex Networksp. 185
Definitions and measures of complex networksp. 186
Unweighted graphsp. 186
Weighted graphsp. 190
Coupling schemes in latticesp. 192
The master stability functionp. 193
Key elements for the assessing of synchronizabilityp. 195
Coupling matrices with a real spectrap. 196
Numerical simulationsp. 198
Coupling matrices with a complex spectrap. 202
Networks with degree-degree correlationp. 206
Synchronization in networks of phase oscillatorsp. 210
Synchronization in dynamical networksp. 212
Synchronization and modular structuresp. 222
Referencesp. 229
Subject Indexp. 241
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780444527431
ISBN-10: 0444527435
Series: Monograph Series on Nonlinear Science and Complexity
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 258
Published: 1st March 2008
Publisher: Elsevier Science & Technology
Country of Publication: GB
Dimensions (cm): 22.5 x 14.9  x 1.68
Weight (kg): 0.55
Edition Number: 1