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 infiuences the dynamical properties, we study the relaxation dynamics in a zero range process on weighted scale-tree 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.