Research On Synchronization Of Dynamical Systems On Complex Networks

It is well known that most of studies about complex networks have focused on the relationship between the network topology and synchronizability. According to the results of recent research, many scholars begin to study on how to improve the synchronizability of complex networks as a matter of convenience to control the synchronizability, such as traffic flow, epidemic spread, and so on. We have studied the synchronizability of the Generalized Deactivation Networks and Random Apollonian Networks without changing their degree distribution, and find that both of their synchronizability can be improved by adjusting the structure parameters.Firstly, we have studied the synchronizability of the Generalized Deactivation Networks and find that the synchronizability of this network is very sensitive to the number of active nodes M and the structure perturbation p. The larger M and p will lead to better synchronizability. Because when M and p larger means the smaller clustering coefficient C, which will lead to better synchronizability. So we can effectively improve synchronizability of the Generalized Deactivation Networks by adjusting the structure parameters——the number of active nodes M and the structure perturbation p. Furthermore, we find the proportional relationship between the eigenratio R and the M and p.Secondly, we have studied the complex networks named Random Apollonian Networks by using random interchange algorithm to change clustering coefficient C, and find that with the decreasing of clustering coefficient C the synchronizability will increase, especially when clustering coefficient C is large.According to the study of Generalized Deactivation Networks and Random Apollonian Networks we find that the smaller clustering coefficient will lead to better synchronizability. Our work is not only meaningful to theoretical interest, but also to the practical value. The effects of topological structure on network synchronizability may provide us a guideline to design algorithm aiming at enhancing or reducing the network synchronizability. Furthermore, we had a pilot study on the relationship between synchronization process and topological scales in complex networks, and proposed the target and task of next step of research.