Synchronization in Complex Networks

✍ Scribed by Xin Biao Lu, Bu Zhi Qin

• Publisher: Nova Science Pub Inc
• Year: 2011
• Tongue: English
• Leaves: 146
• Category: Library

✦ Synopsis

This book discusses the synchronisation in complex networks. At first, the basic concepts of complex networks, including the description of the network, the degree of the node, clustering coefficient, and the average path length are introduced. When the initial states of nodes are near enough to synchronisation manifold, the master stability function method is applied to analyse its local stability. However, when the initial states of nodes are randomly distributed, the Lyapunov function method is used to analyse the global stability of synchronisation manifold. Furthermore, the connection graph stability method is used to investigate the global stability of synchronisation in complex networks with time-varying network topology.

✦ Table of Contents

TITLE PAGE......Page 4
COPYRIGHT......Page 5
CONTENTS......Page 6
PREFACE......Page 8
1.1. INTRODUCTION......Page 10
1.2. BASIC CONCEPT OF NETWORK......Page 12
1.2.2. The Average Path Length......Page 13
1.2.4. Betweenness......Page 14
1.3. COMPLETE SYNCHRONIZATION IN COMPLEX NETWORK......Page 15
1.3.1. Master Stability Function......Page 16
1.3.2. Synchronization of Un-weighted Networks......Page 21
1.3.3.1. Adjust Node Degree......Page 22
1.3.3.2. Adjust Coupling Direction and Edge Information......Page 25
1.3.3.3. Optimal Synchronization of Weighted Networks......Page 26
1.3.3.4. Transition from Non-synchronization to Synchronization......Page 27
2.1. INTRODUCTION......Page 32
2.2. ADAPTIVE SYNCHRONIZATION WITH UNKNOWN NETWORK TOPOLOGIES......Page 33
2.2. Local Synchronization......Page 34
2.2.2. Global Synchronization......Page 37
2.3.1. Global Information......Page 41
2.3.2. Local Information......Page 42
2.3.2. Vertex-based Strategy......Page 43
2.3.2.2. Edge-based Strategy......Page 44
3.1. INTRODUCTION......Page 50
3.2. SELECT APPRECIATE COUPLING MATRIX......Page 51
3.3. ADD SIMPLE CONTROLLERS......Page 54
3.3.1. Local Stability Analysis......Page 57
3.3.2. Global Stability Analysis......Page 59
3.3.3. Simulation Results......Page 60
3.4. ADAPTIVE CLUSTER SYNCHRONIZATION OF COMPLEX NETWORKS......Page 63
3.4.1. Adaptive Strategy in Cluster Synchronization......Page 64
3.4.2. Global Stability Analysis of Cluster Synchronization......Page 65
3.4.3.1. BA Scale-free Network without Noise......Page 67
3.4.3.2. BA Scale-free Network with Noise......Page 70
3.4.3. Nonidentical Oscillators......Page 72
4.1. INTRODUCTION......Page 76
4.2. CONTROL A GENERAL DYNAMICAL NETWORK TO A HOMOGENEOUS EQUILIBRIUM POINT......Page 77
4.3. CONTROL A GENERAL DYNAMICAL NETWORK TO SYNCHRONIZATION STATE......Page 81
4.4. CONTROLLABILITY OF PINNING CONTROL......Page 85
4.5. CONTROL A NETWORK TO A HETEROGENEOUS EQUILIBRIUM POINT......Page 87
4.5.1. Open-loop Constant Control......Page 88
4.5.2.1. Local Stability Analysis......Page 91
4.5.2.2. Global Stability Analysis......Page 96
4.5.2.3. Simulation Results......Page 99
5.1. INTRODUCTION......Page 102
5.2. LOCAL SYNCHRONIZATION OF TIME VARYING COMPLEX NETWORKS......Page 103
5.3.1. Stability Analysis of Global Synchronization......Page 104
5.3.2.1. Average Model......Page 108
5.3.2.2. Blinking Small World Network......Page 109
5.4.1. Local Synchronization of Complex Networks......Page 112
5.4.2. Global Synchronization of Directed Networks......Page 117
5.4.2.2. Switching Topologies......Page 118
5.4.4.3. Simulation Results......Page 125
ACKNOWLEDGMENTS......Page 130
REFERENCES......Page 132
INDEX......Page 144