The Study On Synchronization Of Complex Dynamical Networks

Complex networks have been considered as a new subject for researching complex systems. Many complex system is composed of interacted individuals, which can be naturally represented by graphs with individuals denoted by nodes and interaction by links, for example Internet, World Wide Web, the power grid, railway networks, road networks and so on. The ultimate goal of studying complex networks is to understand how topological properties affect the dynamical processes taking place on them. Synchronization is a common dynamical behavior in complex networks, is also the base to understand harmonious phenomenon. According research of synchronization on complex networks, on the one side, we can understand topological properties affect synchronization on them, on the other hand, we can enhance the synchronous ability of networks when synchronization is advantaged, reduce the synchronous ability of networks when synchronization is disadvantaged. Therefore, researching on synchronization on complex networks provided with great theory sense and application value.In this paper, we used theory analysis and numerical simulation method to study synchronization on complex networks. The main contents in this thesis can be summarized as follows:1.Adding weigh to non-weighed BA networks to get a weigh BA distribution,link weigh distribution also represent power-law. Compare to non-weighed BA networks, when in the same network magnitude, for dynamics systems with unbounded stable synchronization region, the synchronization of the weighed BA networks enhance.2.We bring forward a network, its average degree linearly increase with network size , but other network parameter not change or change little with network size, and research its synchronous ability. Our research indicate that: for with unbounded stable synchronization region system, synchronous ability of networks linearly increases with average degree; but for with unbounded stable synchronization region system, synchronous ability of networks is almost not change.3.We bring forward a network, for different size networks, the ratio long-rule links with the total links and average degree hold invariability, and research its synchronous ability. Our research indicate that, for both networks with bounded stable synchronization region and unbounded stable synchronization region, for large networks, synchronous ability of networks is almost not change, and by add weigh to network, for unbounded stable synchronization region systems, synchronous ability of networks can enhance much.4.Research the synchronization transition from scale-free network to random network. Our research indicate that, for unbounded stable synchronization region system, synchronous ability of networks fluctuate in a small region, it is almost not change; but for with bounded stable synchronization region, synchronous ability of networks can enhance gradually.