What is included with this book?
Preface | p. ix |
Introduction | p. 1 |
Identical Systems | p. 9 |
Complete synchronization | p. 9 |
The PC configuration | p. 11 |
The APD configuration | p. 14 |
Bidirectional coupling configurations | p. 15 |
The stability of the synchronized motion | p. 17 |
The master stability function | p. 20 |
The case of time continuous systems | p. 20 |
The master stability function for coupled maps | p. 25 |
Assessing the synchronizability | p. 25 |
Nonidentical Systems | p. 31 |
Phase synchronization of chaotic systems | p. 33 |
Synchronization of periodic oscillators | p. 33 |
Phase of chaotic signals | p. 36 |
Phase entrainment of externally driven chaotic oscillators | p. 41 |
Phase synchronization of coupled chaotic oscillators | p. 45 |
Transition to phase synchronization of chaos | p. 47 |
Experimental verification of the transition to phase synchronization | p. 49 |
Ring intermittency at the transition to phase synchronization | p. 53 |
Imperfect phase synchronization | p. 58 |
Lag synchronization of chaotic oscillators | p. 61 |
Intermittent lag synchronization | p. 63 |
Phase synchronization of nonautonomous chaotic oscillators | p. 69 |
Generalized synchronization | p. 74 |
A mathematical definition of synchronization | p. 78 |
Synchronization of structurally nonequivalent systems | p. 83 |
From chaotic to periodic synchronized states | p. 85 |
Systems with coexisting attractors | p. 88 |
Methods and tools for detecting synchronized states | p. 94 |
Detection of a functional relationship | p. 95 |
Embedding and multivariate data | p. 96 |
Interdependence between signals | p. 98 |
Predictability of time series | p. 99 |
Coupling direction | p. 101 |
Detection of phase synchronization | p. 101 |
Detection of local synchronization | p. 104 |
Effects of Noise | p. 111 |
Noise-induced complete synchronization of identical chaotic oscillators | p. 112 |
Noise induced phase synchronization of nonidentical chaotic systems | p. 117 |
Noise enhanced phase synchronization in weakly coupled chaotic oscillators | p. 120 |
Constructive noise effects in systems with noncoherent phase dynamics | p. 122 |
Noise-induced changes in time scale and coherence resonance | p. 124 |
Noise-induced complete synchronization | p. 126 |
Noise-enhanced phase synchronization, deterministic and stochastic resonance | p. 129 |
Distributed and Extended Systems | p. 135 |
Synchronization in a chain of coupled circle maps | p. 136 |
Phase synchronization phenomena in a chain of nonidentical phase coherent oscillators | p. 140 |
Collective phase locked states in chains of phase coherent chaotic oscillators | p. 142 |
In phase and anti-phase synchronization in chains of homoclinic oscillators | p. 146 |
Synchronization domains and their competition | p. 151 |
Synchronization in continuous extended systems | p. 157 |
Asymmetric coupling effects | p. 164 |
Defect enhanced anomaly in asymmetrically coupled spatially extended systems | p. 173 |
Convective instabilities of synchronization in space distributed and extended systems | p. 178 |
Complex Networks | p. 185 |
Definitions and measures of complex networks | p. 186 |
Unweighted graphs | p. 186 |
Weighted graphs | p. 190 |
Coupling schemes in lattices | p. 192 |
The master stability function | p. 193 |
Key elements for the assessing of synchronizability | p. 195 |
Coupling matrices with a real spectra | p. 196 |
Numerical simulations | p. 198 |
Coupling matrices with a complex spectra | p. 202 |
Networks with degree-degree correlation | p. 206 |
Synchronization in networks of phase oscillators | p. 210 |
Synchronization in dynamical networks | p. 212 |
Synchronization and modular structures | p. 222 |
References | p. 229 |
Subject Index | p. 241 |
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