Weighted scale-free networks with variable power-law exponents

We present a weighted scale-free network model, in which the power-law exponents can be controlled by the model parameters. The network is generated through the weight-driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links. The simplicity of the model enables us to derive analytically the various statistical properties, such as the distributions of degree, strength, and weight, the degree-strength and degree-weight relationship, and the dependencies of these power-law exponents on the model parameters. Finally, we demonstrate that networks of words, coauthorship of researchers, and collaboration of actor/actresses are quantitatively well described by this model.     

Effects of Scale-Free Topological Properties on Dynamical Synchronization and Control in Coupled Map Lattices

In the paper,we study effects of scale-free (SF) topology on dynamical synchronization and control in coupled map lattices (CML).Our strategy is to apply three feedback control methods,including constant feedback and two types of time-delayed feedback,to a small fraction of network nodes to reach desired synchronous state.Two controlled bifurcation diagrams verses feedback strength are obtained respectively.It is found that the value of critical feedback strength γc for the first time-delayed feedback control is increased linearly as ε is increased linearly.The CML with SF loses synchronization and intermittency occurs if γ,＞γc.Numerical examples are presented to demonstrate all results.     

Relaxation Dynamics in Condensation on Weighted Scale-Free Networks

Most of the realistic networks are weighted scale-free networks. How this structure influences the condensation on it is a challenging problem. Recently, we make a first step to discuss its condensation [Phys. Rev. E 74 （2006） 036101] and here we focus on its evolutionary process of phase transition. In order to show how the weighted transport influences the dynamical properties, we study the relaxation dynamics in a zero range process on weighted scale-free networks. We find that there is a hierarchical relaxation dynamics in the evolution and there is a scaling relation between the relaxation time and the jumping exponent. The relaxation dynamics can be illustrated by a mean-field equation. The theoretical predictions are confirmed by our numerical simulations.