The Self-organized Criticality And Opinion Dynamics On Complex Networks

Many complex systems arising from nature and human society can be described as complex networks. A lot of experimental works show that real complex networks share some distinctive characteristic properties, such as the small-world effect, scale-free property and the hierarchical structure, which differ from the random network and the regular lattice. The topology structure of complex networks has been studied, which is helpful for us to search the dynamics of and on complex networks. In this paper, we focus on the interaction between the complex network structure and the dynamics on complex networks, and study the emergence of some distinctive characteristic properties in complex networks from the viewpoint of dynamics.The results of innovative research are shown as follows:1. To analyze the effects of complex network structure on fractal dimension. Firstly, the fractal dimensions of real complex networks are studied by means of Shanker's defini-tion. Secondly, the effect of the shortcuts in small-world network on the fractal dimension is shown through the relation between the fractal dimension df and the shortcuts (Np), which is given by the method of nonlinear fitting. Finally, the effect of the regular lattice size N on its fractal dimension is analyzed through exact calculation.2. To study the China Railway Network(CRN) by proposing the weighted method based on the trains'real kinematics. Firstly, the degree distribution and the degree-degree correlation of CRN in space L are studied. Then, the weighted property of CRN is analyzed according to the trains' real kinematics. The contribution of train j to terminal station i is 1/nj(i), where nj(i) is the number of stations that train j passes. Here, the definition of weight makes up the shortage of network topology analysis in the abstract space (spaces L and P).3. To analyze how the heterogeneity of complex networks affects the dynamics that occurs on complex networks. We analyze the Bak-Sneppen evolution model on static scale-free networks, where a tunable parameter a is defined to describe the heterogeneous prop-erty of complex network. The larger a is, the more heterogeneous the network is. Our study shows that the critical average fitness * decreases with a increasing. On the other hand, the exponentτof the 0 avalanche decreases in a form of stair-case with a increas-ing. Combining epidemic spreading dynamics on the static scale-free networks and theτexponent, the scale free networks can be divided into three classes:random class, linear class and physical class. Then, extended Deffuant models on regular lattice, small-world networks and scale-free networks are studied, where the bifurcation phenomena is found. Through analyzing the relationship between the opinion, degree and theεin the minority clusters, we find the formation process of opinion in small-world networks is different from that in scale-free networks, which is also found in the synchronization phenomena in both networks.4. To analyze the effect of the shortcuts in small-world network on the opinion for-mation dynamics. According to the Ising model in statistical physics, we investigate the binary opinion formation dynamic on small-world network. The magnetization, spatial correlation and temporal correlation are studied. Our results show that the shortcuts en-hance the ability of long-range interactions which can drive the system towards reaching the consensus state. On the other hand, the phase transition in the small-world network which is built on one dimension substrate is a pseudo one.5. To analyze the emergence of community in the adaptive network. A simple adap-tive network model is proposed. The edge between active vertices is broken when the difference between two vertices' opinion is greater than the confidence parameterε; Other-wise, each opinion moves partly in favor of the direction of the other. The rewiring of the broken edge follows the rules of the rewiring of local attachment (RLA) and the rewiring of global rewiring (RGA). All is mentioned above shows the interaction between the dynamics of complex network structure and the dynamics on complex network. Through simulations, we find that the RGA enhances the ability of the system reaching the phase transition, and the RLA enhances the formation of community structure in complex networks.