| With the development of computer science and technology, we are challenged by complex networks from different background such as society, economics, brain networks, etc. These networks share some common network structures and have some similar dynamics occurring upon them, among which synchronization is an important dynamic. However, to better utilize synchronization, we sometime need to enhance or suppress synchronization, promoting us to control synchronization. Since both synchronization and control problems are closely related with network structure, network structure, synchronization and control are usually investigated together. The detailed contents and main results of my thesis are summarized as follows:1. Influences of community structure on information spreading are studied. Based on local routing strategy, information capacity of networks with different community structure is investigated and the results show that network capacity decreases as the strength of community structure increases. If all nodes have identical capacity, information should be transferred to neighbor nodes with low degree.2. I have studied the influence of degree mixing pattern on synchronization paths. Synchronization paths of both BA scale-free and ER random networks are investigated. We find that in assortative scale-free networks, synchronization is achieved by the merging of small synchronizing clusters. But in disassortative scale-free networks, increasing of the largest synchronizing cluster leads to col-lective synchronization. However, the degree mixing pattern does not influence synchronization paths in ER networks.3. Community structure is detected by local synchronization. We propose an improved synchronization model that could suppress collective synchroniza-tion and lock local synchronization automatically, and communities emerge in the paths. The results show that nodes in the same community have similar phas-es and nodes across different communities have different phases. The proposed method has better performance than traditional methods.4. Synchronization is tamed by pinning control and optimal pinning control is studied. Through theory of linear matrix inequality, the optimal feedback gains of each node is obtained to evaluate their importance in pinning control. The results show that some low-degree nodes have high feedback gains and some high-degree nodes have low feedback gains, which indicates that optimal pinning nodes should contain both high-degree and low-degree nodes. Further, it is found that increasing the sparsity of pinning nodes could increase the controllability in real-world networks. Then a fast and effective method is proposed to select pinning nodes, which outperforms traditional large-degree method that selects pinning nodes according to the degree of nodes. |
