Study On Scale-free Network And Its Synchronization

Synchronization process in scale-free networks and weighted evolving scale-freenetwork model are studied in this thesis, separated into the following three parts:In the first part, a comment on 《Hub synchronization in scale-free networks》[Phys.Rev. E82,036201(2010)] is made, and synchronization process in scale-free networks isstudied. In 《Hub synchronization in scale-free networks》, Tiago Pereira reported hubsundergo a transition to synchronization in scale-free network while the other nodes remainunsynchronized. The author also claimed that "This conclusion only holds for large scale SFnetworks." and "For large scale-free networks the coupling term can be made as small as onewishes wheneverk nis large enough." Actually, it is not the case. We rebut this paper fromthe research methods to the conclusion and the numerical simulation through theoretical proofand simulation. In order to further reveal the characteristic that synchronization process inscale-free networks should be present, we apply the nonlinear system theory and the stabilitytheory to study the synchronization process in scale-free networks, introduce nonlineardynamics on each node and perform stability analysis to determine when the nodessynchronize, in addition, we analysis the difference of the research methods betweenscale-free networks and general continuous coupling networks. The conclusion is shown thatheterogeneity of the degree distribution in scale-free networks not only inhibits the globalsynchronization, but also leads to a hierarchical transition toward further synchronization, andTiago Pereira’s conclusion and simulation result is just a one-sided phenomenon ofsynchronization process.In the second part, because most of the existing typical weighted networks aremonotonous growth model while the evolutionary process of the actual network is tortuous. Inorder to better simulate the evolutionary process of the actual networks, and generatenetworks with the topology characteristics of the actual networks, we extend the concepts ofthe preferential attachment schemes and the preferential strengthening schemes used in theevolutionary model of the existing typical weighted networks, and propose an improved evolutionary model based on process. We change the process parameters of the evolutionaryone by one to carry out the simulations, and compare the simulation results to study theeffects of various process parameters on the network topology features and networksynchronization stability.In the third part, we take the process-based weighted scale-free network model as anetwork model to study the differences of the synchronization process in scale-free networkbefore and after the introduction of the weight to the edge.