  The dynamics of zero-range processes on complex networks is expected to be
influenced by the topological structure of underlying networks. A real space
complete condensation phase transition in the stationary state may occur. We
have studied the finite density effects of the condensation transition in both
the stationary and dynamical zero-range process on scale-free networks. By
means of grand canonical ensemble method, we predict analytically the scaling
laws of the average occupation number with respect to the finite density for
the steady state. We further explore the relaxation dynamics of the
condensation phase transition. By applying the hierarchical evolution and
scaling ansatz, a scaling law for the relaxation dynamics is predicted. Monte
Carlo simulations are performed and the predicted density scaling laws are
nicely validated.
