Paths To Synchronization On Complex Networks With External Drive

In recent years, the research on complex networks has got rapid development and caught the attention of the researchers in biology, computer science, physics, social science and so on. Many systems in real life can be described by complex networks. And the phenomenon in practical system can be described by the dynamics behavior of oscillators. Complex network is a system composed by a large number of nodes and the connection between them. When we carry on the discussion about real problems, agents in real networks can be described as nodes, and the interaction of agents can be described as the edges. For example, the nodes can represent the individuals in the social networks, while the edges can represent the interaction between the individuals. Since the complex network topology is determined by its network structure, this spurred the study of complex network structure, and the interest of it encourages us to overcome difficulties in our study.Synchronization is one of the common dynamic phenomena in complex networks, which is also common in human society. With the increasing concern about complex network, people have made a lot of researches on studying the dynamical behavior of complex networks. They have studied the network synchronization characteristics on different network topology. On the basis of their researches, this paper mainly studied the dynamics of the Kuramoto Model on complex networks with part of the oscillators subjected to an external drive. It is found that the mutual synchronization is attracted to the drive when the frequency of the drive is close to the mean frequency of oscillators and, otherwise, mutual synchronization coexists with the driven synchronization. We also find that the synchronization between the mutual synchronization and the driven synchronization is dependent on the network topology when the coupling strength among oscillators is far away from the global synchronization in the absence of the drive. The transition is continuous on Erdos-Renyi networks while it is discontinuous on Scale-Free networks.