Complex Network Synchronization Study

Currently, research on complex networks just begins to emerge and attracts much attention. In fact, complex networks are on our life nowadays. In the paper, we applied theories of nonlinear dynamics, statistical physics, matrix analysis, and used computer calculating method to study synchronization on complex networks. Based on relational network models, we analyzed the effects of topology and weight distribution of a network on complex network. These researches have great significance for the understanding and practical applications of the synchronization in real networks.The main contents and originalities in this thesis can be summarized as follows:1. The real-world networks, especially the neural networks, are weighted and directed. On the other hand, recent research shows that many biological neural networks including brain cortical networks are small-world networks and it has found the rhythmic phenomena in the brain. So we studied the complete and phase synchronization in weighted small-world neuron network. We obtained the synchronization conditions of the complete and phase synchronization in weighted small-world neural networks. The results among neural oscillators presented in this paper should be useful for the understanding of the rhythmic phenomena and information processing in the brain. We also studied the effects of the weight distribution on complete synchronization. We found that the synchronizability is weaker in a small-world network with power-law weight distribution than that with random weight distribution. The results obtained here are more realistic than previous works. And the synchronization results in networks of coupled chaotic oscillators presented in this paper should be useful for the understanding of the dynamic processing in many real-world networks.2. It is also found that many complex networks exhibit community structures. This is, the dynamics in the communities would be different from it in the networks. So we studied the collective dynamic behavior of such network. We found that the phase synchronization was first realized among the more tightly interconnected nodes within communities. Then the whole network reached the state of synchronization. The results should be use for the understanding of the dynamic processing in complex networks with community structure.