Synchronization Of The Dynamical Systems In The Complex Networks

Inspired by the current rapid development of the research field on controlling the synchronization of chaotic oscillators in the complex networks, we carried out the research work on the topological characters and the synchronizability of the networks as well as their relationships. The paper can be divided into three parts.In the first part, we discussed the research background of the complex networks theory and its fundamental theory, such as the networks' topological parameters, the mean shortest path-length, the clustering coefficient, the maximal load of the link in the networks, etc. We also discussed some basic networks topologies, which have been widely studied and also serve as the base of our research work.In the second part, based on the real data about the Short Message Networks (SMN), we investigated the growing process and topological features of SMN. Our simulations show that the networks' degree distribution, average degree and the correlation between the nodes' degree and its time in the network are different from those of previous networks models. Based on these characteristics of SMN, we consider a new type of network growing protocol: local-preference connecting protocol. The numerical results show that the networks generated from our model are more representative in simulating real networks represented by SMN when compared with other networks models.In the last part of this paper, we studied the stability problem of the chaos synchronization in different kinds of complex networks. We have studied the topologies of different networks comprising many chaotic oscillators, and investigated the relations between the topological parameters and the synchronizability of these chaotic oscillators for the purpose of finding the best network for synchronization of chaotic oscillators. Specifically, we studied chaotic synchronization in complex networks by using an evolutionary model and developed an optimization algorithm capable of increasing synchronizability of networks. We find that while the relationships between the networks' structural and dynamical parameters are complicated, the winner through the evolution is a homogeneous network in which each node behaves the same geometrically and topologically. The homogeneous network has the advantages in that the traffic flow through any node is almost the same and it avoids hubs and boundary nodes in the networks.