Title Page
ABSTRACTS
Contents
Chapter 1. THE INFLUENCE OF DIRECTIONALITY ON THE GRIFFITHS PHASES 9
1.1. INTRODUCTION 9
1.2. MODELS 11
1.2.1. Contact process and quenched contact process 11
1.2.2. Complex network structures 12
1.3. RESULTS 14
1.3.1. The Griffiths phases due to quenched contact process in directed random networks 14
1.3.2. The Griffiths phases due to quenched contact process in directed scale-free networks 19
1.3.3. The Griffiths phases in the directed small world networks 22
1.3.4. The Griffiths phases in directed hierarchical modular networks 25
1.4. DISCUSSION AND CONCLUSION 31
Chapter 2. THE INFLUENCE OF MODULARITY ON THE EXPLOSIVE SYNCHRONIZATION IN SCALE-FREE NETWORKS 33
2.1. INTRODUCTION 33
2.2. METHODS 36
2.2.1. The 2-module modular scale-free networks 36
2.2.2. The Kuramoto model 37
2.3. RESULTS 39
2.3.1. The order parameters in the case of the hub-to-hub connection 39
2.3.2. The order parameters in the case of hub-to-peripheral connection 48
2.3.3. The order parameters in the case of peripheral-to-peripheral connection 56
2.3.4. The formation of the cusp at the low inter-modular connected edges Eint[이미지참조] 64
2.3.5. The variation of the cusp's position with the difference of the hubs' degrees 69
2.4. CONCLUSIONS 73
Chapter 3. THE INFLUENCE OF MODULARITY ON THE EXPLOSIVE SYNCHRONIZATION IN MODULAR NETWORKS 75
3.1. INTRODUCTION 75
3.2. METHODS 76
3.3. RESULTS 77
3.3.1. The order parameter at the upper critical coupling strength 77
3.3.2. The little impact of the number of inter-modular connections on the local transition in each module 86
3.4. CONCLUSION 90
CONCLUSION 91
REFERENCES 93