SYNCHRONIZATION IN COMPLEX NETWORKS

SYNCHRONIZATION IN COMPLEX NETWORKS

CONTENTS

PREFACE

Chapter 1 SUMMARIZATION OF SYNCHRONIZATION IN COMPLEX NETWORK

Abstract

1.1. Introduction

1.2. Basic Concept of Network

1.2.1. The Graph Description of Network

1.2.2. The Average Path Length

1.2.3. Clustering Coefficient

1.2.4. Betweenness

1.2.5. Assortative Coefficient

1.3. Complete Synchronization in Complex Network

1.3.1. Master Stability Function

1.3.2. Synchronization of Un-weighted Networks

1.3.3. Synchronization of Weighted Networks

1.3.3.1. Adjust Node Degree

1.3.3.2. Adjust Coupling Direction and Edge Information

1.3.3.3. Optimal Synchronization of Weighted Networks

1.3.3.4. Transition from Non-synchronization to Synchronization

Chapter 2 ADAPTIVE SYNCHRONIZATION OF COMPLEX NETWORKS

Abstract

2.1. Introduction

2.2. Adaptive Synchronization with Unknown Network Topologies

2.2. Local Synchronization

2.2.2. Global Synchronization

2.3 Adaptive Synchronization with Known Network Topologies

2.3.1. Global Information

2.3.2. Local Information

2.3.2. Vertex-based Strategy

2.3.2.2. Edge-based Strategy

Chapter 3 CLUSTER SYNCHRONIZATION IN COMPLEX NETWORKS

Abstract

3.1. Introduction

3.2. Select Appreciate Coupling Matrix

3.3. Add Simple Controllers

3.3.1. Local Stability Analysis

3.3.2. Global Stability Analysis

3.3.3. Simulation Results

3.4. Adaptive Cluster Synchronization of Complex Networks

3.4.1. Adaptive Strategy in Cluster Synchronization

3.4.2. Global Stability Analysis of Cluster Synchronization

3.4.3. Simulation Results

3.4.3.1. BA Scale-free Network without Noise

3.4.3.2. BA Scale-free Network with Noise

3.4.3. Nonidentical Oscillators

Chapter 4 CONTROL OF COMPLEX DYNAMICAL NETWORKS

Abstract

4.1. Introduction

4.2. Control a General Dynamical Network to a Homogeneous Equilibrium Point

4.3. Control a General Dynamical Network to Synchronization State

4.4. Controllability of Pinning Control

4.5. Control a Network to a Heterogeneous Equilibrium Point

4.5.1. Open-loop Constant Control

4.5.2. Feedback Pinning Control

4.5.2.1. Local Stability Analysis

4.5.2.2. Global Stability Analysis

4.5.2.3. Simulation Results

Chapter 5 SYNCHRONIZATION OF TIME VARYING COMPLEX NETWORKS

Abstract

5.1. Introduction

5.2. Local Synchronization of Time Varying Complex Networks

5.3. Connection Graph Stability Method

5.3.1. Stability Analysis of Global Synchronization

5.3.2. Application of Connection Graph Stability Method

5.3.2.1. Average Model

5.3.2.2. Blinking Small World Network

5.4. Fast Switching Synchronization of Time Varying Complex Networks

5.4.1. Local Synchronization of Complex Networks

5.4.2. Global Synchronization of Directed Networks

5.4.2.1. Fixed Topology

5.4.2.2. Switching Topologies

5.4.4.3. Simulation Results

ACKNOWLEDGMENTS

REFERENCES

INDEX

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