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E-raamat: Synchronization: From Coupled Systems to Complex Networks

, (University of Warwick), (University College Cork), (Consiglio Nazionale delle Ricerche (CNR), Rome)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 29-Mar-2018
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108640039
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Synchronization: From Coupled Systems to Complex NetworksSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 29-Mar-2018
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108640039
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A modern introduction to synchronization phenomena, this text presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The book describes some of the main mechanisms of collective behaviour in dynamical systems, including simple coupled systems, chaotic systems, and systems of infinite-dimension. After introducing the reader to the basic concepts of nonlinear dynamics, the book explores the main synchronized states of coupled systems and describes the influence of noise and the occurrence of synchronous motion in multistable and spatially-extended systems. Finally, the authors discuss the underlying principles of collective dynamics on complex networks, providing an understanding of how networked systems are able to function as a whole in order to process information, perform coordinated tasks, and respond collectively to external perturbations. The demonstrations, numerous illustrations and application examples will help advanced graduate students and researchers gain an organic and complete understanding of the subject.

A modern introduction to synchronization phenomena, this book presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The demonstrations, numerous illustrations and application examples will help advanced graduate students and researchers gain an organic understanding of the subject.

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A modern introduction to synchronization phenomena, combining the development of deep mathematical concepts with illustrative examples and practical applications.
Preface ix
1 Introduction and Main Concepts
1(20)
1.1 Dynamical Systems
1(4)
1.1.1 Linear Dynamical Systems
2(1)
1.1.2 Nonlinear Dynamical Systems
3(1)
1.1.3 Autonomous and Nonautonomous Systems
4(1)
1.1.4 Conservative and Dissipative Systems
4(1)
1.2 Chaotic Systems
5(4)
1.2.1 Time Series
6(1)
1.2.2 Phase Space
6(2)
1.2.3 Power Spectrum
8(1)
1.3 Attractors
9(2)
1.3.1 Types of Attractors
9(1)
1.3.2 Basins of Attraction and Poincare Maps
10(1)
1.4 Stability of Dynamical Systems
11(10)
1.4.1 Linear Stability Analysis
11(2)
1.4.2 Lyapunov Exponents
13(1)
1.4.3 Bifurcations
14(7)
2 Low-Dimensional Systems
21(56)
2.1 A Brief History of Synchronization
21(2)
2.2 Types of Coupling
23(3)
2.3 Phase Oscillators
26(8)
2.3.1 Unidirectionally Coupled Phase Oscillators
28(3)
2.3.2 Mutually Coupled Phase Oscillators
31(1)
2.3.3 Frequency-Splitting Bifurcation
31(3)
2.4 Complete Synchronization
34(13)
2.4.1 Measures of Complete Synchronization
34(1)
2.4.2 Bidirectional Coupling
35(1)
2.4.3 Unidirectional Coupling
36(3)
2.4.4 Conditional Lyapunov Exponents for Discrete Systems
39(2)
2.4.5 Example of Coupled Rossler-Like Oscillators
41(4)
2.4.6 Stability of the Synchronization Manifold
45(2)
2.5 Phase Synchronization
47(13)
2.5.1 Defining Phases in Chaotic Systems
47(5)
2.5.2 Measures of Phase Synchronization
52(3)
2.5.3 Example: Ring of Rossler Oscillators
55(5)
2.6 Lag and Anticipating Synchronization
60(4)
2.7 Coherence Enhancement
64(4)
2.7.1 Deterministic Coherence Resonance
66(1)
2.7.2 Stabilization of Periodic Orbits in a Ring of Coupled Chaotic Oscillators
66(2)
2.8 Generalized Synchronization
68(7)
2.8.1 Generalized Synchronization in Unidirectionally Coupled Systems
69(5)
2.8.2 Generalized Synchronization in Bidirectionally Coupled Systems
74(1)
2.9 A Unifying Mathematical Framework for Synchronization
75(2)
3 Multistable Systems, Coupled Neurons, and Applications
77(47)
3.1 Unidirectionally Coupled Multistable Systems
79(13)
3.1.1 Synchronization States
79(1)
3.1.2 An Example
80(12)
3.2 Systems with a Common External Force: Crowd Formation
92(6)
3.2.1 A Numerical Example
94(4)
3.3 Bidirectionally Coupled Systems
98(3)
3.4 Synchronization of Coupled Neurons
101(11)
3.4.1 Synchronization of Neurons with Memory
102(2)
3.4.2 Synchronization of Neurons with Arbitrary Phase Shift
104(5)
3.4.3 Phase Map
109(3)
3.5 Chaos Synchronization for Secure Communication
112(12)
3.5.1 Communication Using Chaotic Semiconductor Lasers
114(2)
3.5.2 One-Channel Communication Scheme
116(3)
3.5.3 Two-Channel Communication Scheme
119(5)
4 High-Dimensional Systems
124(61)
4.1 The Kuramoto Model
124(20)
4.1.1 Derivation from a Generic Oscillator Model
125(2)
4.1.2 The Case N = 3
127(3)
4.1.3 The Kuramoto Order Parameter
130(2)
4.1.4 Numerical Phenomenology for Large N
132(3)
4.1.5 Theory for Large N
135(6)
4.1.6 Kuramoto Model with Time-Varying Links
141(3)
4.2 High-Dimensional Systems with Spatial Topologies
144(3)
4.2.1 Spatially Discrete versus Spatially Continuous Systems
144(1)
4.2.2 Terminology of Coupling Schemes
145(2)
4.3 Chimera States
147(19)
4.3.1 Numerical Phenomenology of the Classical Chimera State
148(5)
4.3.2 Classical versus Generalized Chimera States
153(7)
4.3.3 Experimental Implementation of Chimera States
160(4)
4.3.4 Theory of Chimeras
164(2)
4.4 Bellerophon States
166(2)
4.5 Oscillation Quenching
168(8)
4.5.1 Amplitude Death
169(4)
4.5.2 Oscillation Death
173(2)
4.5.3 Chimera Death
175(1)
4.6 Auto-Synchronization and Time-Delayed Feedback
176(9)
4.6.1 Chaos Control
177(2)
4.6.2 Experimental Realization
179(1)
4.6.3 Theory
180(5)
5 Complex Networks
185(52)
5.1 Introduction
185(3)
5.2 Master Stability Function
188(7)
5.2.1 Derivation of the Master Stability Function
188(4)
5.2.2 Classes of Synchronizability
192(3)
5.3 Small-World Networks
195(7)
5.3.1 Ring Lattices
196(3)
5.3.2 The Watts--Strogatz Model
199(3)
5.4 Preferential Attachment Networks
202(2)
5.5 Eigenvalue Bounds
204(18)
5.5.1 Minimum Degree Upper Bound for the Spectral Gap
204(3)
5.5.2 Connectivity Lower Bound on the Spectral Gap
207(7)
5.5.3 Diameter Lower Bound for the Spectral Gap
214(4)
5.5.4 Degree Bounds on λN
218(2)
5.5.5 Summary
220(2)
5.6 Enhancing and Optimizing Synchronization of Complex Networks
222(1)
5.7 Explosive Synchronization in Complex Networks
223(1)
5.8 Synchronization in Temporal and Multilayer Networks
224(7)
5.8.1 Time-Varying Networks
224(2)
5.8.2 Synchronization in Multilayer Networks
226(3)
5.8.3 Application of the Master Stability Function to Multistable Dynamical Systems
229(2)
5.9 Single-Oscillator Experiments
231(6)
5.9.1 Experimental Setup
231(1)
5.9.2 General Equation
232(2)
5.9.3 Network of Piecewise Rossler Oscillators
234(1)
5.9.4 Synchronization Error
235(2)
References 237(15)
Index 252
Stefano Boccaletti is Senior Researcher at the Consiglio Nazionale delle Ricerche-Institute for Complex Systems. Previously he has been the Scientific Attache' at the Italian Embassy in Israel,  Full Researcher at the National Institute of Optics in Italy, and Visiting Scientist or Honorary Professor of 7 International Universities. He is the editor of four books and Editor in Chief of Chaos Solitons and Fractals. Alexander N. Pisarchik is Isaac-Peral Chair in Computational Systems Biology at the Center for Biomedical Technology of the Technical University of Madrid. His research interests include chaos theory and applications in optics, electronics, biology and medicine, chaotic cryptography and communication. Charo I. del Genio is Visiting Faculty Member at the University of Warwick and his work primarily focuses on graph theory and complex networks, particularly those with an algorithmic or simulation component. Recently he has been applying methods from network research to the study of biological systems, to explain biomolecular mechanisms and design new antimicrobial drugs. Andreas Amann is a Lecturer at University College Cork and his research interests focus on semiconductor physics, lasers and photonics and more recently, energy harvesting devices. From a mathematical perspective his work concerns synchronization, time delay and complex networks.
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