The Investgation Of Tree-Like Network

In recent years,the concept of network has been proposed and researched and it has been an important tool of revealing the structure and function of each kind of complexity system in nature and human society. In the study of complex networks research, mostly concentrated on small-world networks and scale-free networks. In real complex systems, there are a large number of fractal structures, such as trees, rivers, galaxies, lightning, national organizational systems, management systems. It is well known that fractal structure has self-similarity. In complex networks, tree-like model abound. In this paper, two typical tree-like networks for the study.In this paper we investigate the tree-like network with regular structure first, the structure of such a network has a good self-similarity, also has small-world effect and scale-free property. Next we study the synchronization of the network, when the size is small, only through the coupling between nodes, the network can be synchronized to a stable state, but the synchronization state is still an irregular oscillation. When the scale of the network go a step further expand, only by coupling, the network can not achieve synchronization. We adjust the synchronization scheme, control the main root node of the network, numerical simulation result shows that in this way could maintain the network synchronization if the scale ger further expand. Finally, for the vulnerability of the network to deliberate attack, we improved the model by adding some random connections, the improved network still has the small-world effect and scale-free property;We add weight to the improved network. With this adding-weight method, the maximum weight of the nodes shows exponential growth, which is ubiquitous in social networks.