Research On Dynamical Behaviors Of Complex Networks

As one of the most active areas in the interdisciplinary research field, complex networks attract extensive attentions from various fields of science and engineering. In this dissertation, we perform dynamics study on complex networks. The main contents of this dissertation include: (1) Local and global stability of synchronization in some delayed complex networks; (2) Synchronization and its perturbation of weighted networks with delayed couplings; (3) Phase synchronization and synchronization process in switching networks; (4) Approach to analyze synchronization of coupled map on complex networks; (5) Epidemic spreading on mobile wireless networks.The main contribution in this dissertation can be summarized as follows:1. Local and global synchronization study of delayed complex networksDue to limited transmitting speed and process ability on nodes, usually there are time delays in complex networks. Considering the differences between the factors that induce time delays, we study the synchronization of time-delayed coupled complex networks where the delays are caused by limited transmitting speed and synchronization of coupled time-delayed dynamical systems where the delays are caused by properties of nodes, respectively. For the delayed complex networks with time-varying couplings, we present a new approach to analyze the stability of synchronization manifold by combining subspace decomposition and Lyapunov functions. As to the second case, we derive the criteria for locally asymptotical synchronization and globally exponential synchronization.2. The study of synchronization and its perturbation in weighted complex networks with time delayMany real-world networks are dynamically evolving, for example, new edges are introduced or old edges are removed continually, which certainly will have an effect on network synchronizability. In this dissertation we study the perturbation phenomenon of weighted complex networks with time delay when disturbing the coupling configurations. In the light of theoretical analysis, we obtained the criterion for synchronization which is directly related with network topology. We further investigated the impact of topology on dynamics under small coupling perturbations by applying our theoretical results.3. Phase synchronization study on switching networks of coupled oscillatorsIt is often the case that due to the dynamic nature of each unit's states in some distributed communication systems, the existence of an information channel between a parr of units at each time instance is probabilistic and independent of other channels; hence, the topology of such networks varies over time. Taking this case into account, we study the onset of synchronization in arrays of phase oscillators with switching couplings. We found that the network always can achieve synchronization under fast switches. Moreover, we further studied the role of network topologies in the synchronization process and observed the different synchronization processes between homogeneous networks and heterogeneous networks from our switching network model.4. Study on synchronization of coupled map networks by a new approachConsidering the limitation of existing stability analysis methods for complex network synchronization to some extent, we present a new approach to study the sychronizability by using matrix measure. Through theoretical analysis of coupled discrete maps, we obtained the local and global synchronization criteria which can be easily verified and applied in practice.5. Spreading dynamics study on dynamical complex networksThe effect of network topology on system dynamics can also be manifested in epidemic spreading behaviors. In this dissertation, we present a dynamical complex network model to describe the mobile wireless Ad hoc networks. This model captures the mobility of nodes in networks, channel contention during communicating and limited physical connections. By means of basic SIR model, we studied the spreading dynamics of worms on this model, finding the relationship between the mobility of nodes and epidemic spreading.