Explosive Synchronization And Cascading Failure In Complex Network

The study on complex networks has recently become a hot topic and has significantly deepen our understanding to the real complex systems. Thus it is theoretically and realistically significant to conduct further studies on complex network. The study on the dynamics of complex networks is one of the hottest di-rections in the field of complex networks, where the main topics are synchroniza-tion, phase transition and cascading failure etc. Explosive synchronization exists in some realistic systems, such as the cascading failure of power grid, avalanche effect on multi-networks and the spreading of epidemic, etc. In this thesis, we focus on three topics as follows:explosive synchronization and epidemic spread-ing on interdependent co-evolving networks, discussion on condensation phase transition in networks, modeling the cascading failure of power grids by a circuit approach. The thesis is organized as follows:The first chapter is an introduction. In this chapter, we first introduce the basic knowledge and research background, and then describe our work briefly.In the second chapter, we study the explosive synchronization and epidemic spreading on interdependent co-evolving networks. Since many realistic dynam-ics are based on complicated networks such as the co-evolving networks with mutual correlation, it is very important to investigate this kind of systems. We here study this kind of realistic dynamics by presenting a network model consist-ing of two interdependent subnetworks, which have the same power-law degree distribution. We focus on two typical dynamics, i.e., the explosive synchroniza-tion and epidemic spreading. For the former, we show that the explosive synchro-nization can exist for a large class of co-evolving networks with scale-free distri-butions, thus extending the condition of explosive synchronization from strong correlation with Ui=ki to weak correlation with ωi=f(ki). For the latter, we find that the subnetwork of information will significantly influence the epidemic spreading on the subnetwork of contact through the correlation between them.In the third chapter, we study the condensation phase transition in networks. We analyze the condensation phase transitions in out-of-equilibrium complex networks in a unifying framework which includes the nonlinear model and the fitness model as its appropriate limits. We show a novel phase structure which depends on both the fitness parameter and the nonlinear exponent. The occur-rence of the condensation phase transitions in the dynamical evolution of the net-work is demonstrated by using Bianconi-Barabasi method. We find that the non-linear and the fitness preferential-attachment mechanisms play important roles in the formation of an interesting phase structure.In the fourth chapter, we study the cascading failure in power grids. It is well known that cascading failure usually happens in networked systems and has re-cently been paid great attention. It is revealed that both perturbations and inten-tional attack can cause cascading failure of the whole network where the topology of single network and the coupling between dependent networks may take a key role. Based on the real data of electric currents in power grids, we here present a dynamics circuit model to study the mechanism of cascading failure, in contrast to the previous static network models. This model considers both the preferen-tial attachment and the geographical factor and thus results in a practical power grids’degree distribution with both power-law and local community structure. We find that by varying a parameter, this model can show a phenomenon of cas-cading failure in power grids. This work is of significant on the construction of power grid.In the fifth chapter, we summarize obtained results and give an outlook for future studies.