Local Synchronization On Complex Network:Empirical Study,Dynamics And Applications

Benefiting the development of information technology and advance of human civilization, lots of large-scale networks are developed in information, biology, society and economy areas. In contrast to the graph theory and classic social network analysis, it’s a brand new challenge to understand the structure of large-scale networks and dynamics taking place on them. This challenge has attracted great research interests from variety areas in recent decade, which lead to the emergence of complex network theory. One important topic in complex network theory is the relation between structure and dynamics. The relation between net-work structure and local synchronization behaviors are studied via empirical and theoretical way. The empirical study and theoretical analysis both show the co-herence between local network structure and synchronization behavior. Thus the local synchronization is applied for detecting hierarchical structure and navigation based on the coherence. The detailed contents and main results of the thesis are summarized as follow:1、The local synchronization behaviors of human brain is studied through brain functional network. A61-channel ERP data recorded during audio task is used in the first empirical study. The cluster coefficients and sizes of giant com-ponent of brain functional networks under audio task are larger than those under resting state, which indicates different local synchronization behaviors under cog-nitive task and resting state. A238-channel high-resolution ERP data recorded during visual task is used in the second empirical study. The brain functional networks show strong community structures under visual task, which indicates clustering behaviors in local synchronization. In particular, community struc-tures of the brain functional network are compared with anatomical parcellations of the brain cortex. Results show coherence between community structures and anatomical parcellations. The local synchronization behaviors in human brain are tightly connected to the anatomical parcellations and theirs corresponding cognitive functions.2、The dynamics of local synchronization is theoretical studied through mas- ter stability function approach. Since the variance between oscillators is mainly made of the eigenvector corresponding to the weight converging slowest, behaviors in synchronizing process can be predicted by Laplacian eigenvectors of coupling network. Based on this theoretical result, the different local synchronization be-haviors of ER and BA model are explained by the Laplacian eigenvector corre-sponding to the smallest nontrivial eigenvalue. Moreover, the completely different local synchronization behaviors under weak and strong coupling strength of cou-pled oscillators whose master stability function is not monotonic are predicted.3、The local synchronization is applied to detect hierarchical structure in complex networks. The clustering behaviors in local synchronization can be pre-cisely controlled at different levels of hierarchy to detect expected community structure via changing the coupling strength. Numerical simulations on bench-mark and practical networks proved the efficiency of detecting hierarchical struc-ture by local synchronization. At the meantime, it’s also proved that the clustering behaviors do not rely on the dynamics of chaotic oscillators.4、The local synchronization is applied to self-organized reconstruct hidden metric space for navigation on complex networks. The self-organized reconstruc-tion algorithm and navigation are carried out on WS model and generalized BA model to study navigability of small-world networks. Results show that networks display strong navigability only if they show small-world property. The long-range connections play an important role in navigation process.