Clustering - Weighted Synchronization On Small - World Networks

Synchronization phenomena are prevalently existed in science,nature,engineering and social life which play an important role in many systems.Hence understanding the mechanism of the synchronization phenomena is a significant problem.It has been an important issue in nonlinear dynamics.In the last century,most of the researches focus on the networks with fixed regular topology emphasizing the complexity due to the nonlinear dynamics on the nodes,for example,the emerging of the patterns,the spatiotemporal chaos,and so on. Now, there are a lot of work to study synchronous conditions and synchronization capabilities of nonlinear vibration subsystems.In recent years,a large number of studies have shown that the connection of the nodes in complex systems have special properties,such as scale-free,small world,the module features and weighting characteristics and so on. The problems of complex networks is a hot point in recent years,which promotes intersection of different disciplines building bridges for merging between different subjects. Network is closely related to human society, such as financial networks, transportation networks, disease transmission networks and biochemical networks. The main focus of this thesis is to study the effect of the network topology on synchronization.The property of a short average path length and a high clustering coefficient has been widely accepted as the characteristics of small world network.Recently, people found a real weighted small-world structure based on the clustering coefficient weighting. In this article, we take this type of networks as the researches subject.The simulation results show that small world network model can improve the synchronization of networks compared to the previous regular or random networks. This conclusion is consistent with that for unweighted networks.In the same topological structure, weighting results in the slightly decrease of the synchronization capacity.The mechanism for synchronization is investigated and the relationship between the change in the stability of the synchronization due to different weights and topological properties.