Phase Synchronization On Complex Networks

On the basis of some introduction to the basic theories of complex network, the present dissertation studies a kind of community network and the structural properties of this community network; we investigate the phase synchronization on complex networks and mainly focus on the effects which could be caused by different network structure and time delay.Community structure is ubiquitous in real-world networks: individuals tends to form sparsely linked groups, each having dense internal connections. We propose an evolving community network model based on local processes, the addition of new nodes intra-community and the appearance of new links intra- or inter- community. We have done theoretical analysis and numerical simulation that revealed the generalized Power-law degree distribution.We also investigate collective behavior of coupled oscillators on complex networks by means of the Kuramoto model. For globally coupled graph, the phase synchronization will emerge while coupling strength is larger than a critical value. For small-world network and scale-free network, the structural properties are the significant factor which affects synchronizability. We investigate collective behaviors of coupled phase oscillators on an extended network model which can develop two fundamentally different topologies, scale-free or exponential. It is found that system's collective behaviors exhibit strong dependence on local events: addition of new links will improve network synchronizability while rewiring of links will decrease synchronization. The effect of time delay is also introduced into the studies of synchronization. It causes multi-stability on globally coupled graph. The result of numerical simulation on BA network displays new phenomena.