Fluctuation of incoming flux with multiplicative noise on a scale-free network

We study the influence of topology on the dynamical properties of a diffusion process which can be described by a diffusion equation with multiplicative noise on a complex network. From numerical simulations we find that the fluctuation of the incoming mass on a given node of network scales with the average incoming mass, or flux, in a topology-dependent fashion. By combining numerical results with the Langevin equation of the associated process, we show that inhomogeneity of the underlying structure leads to the appearance of distinct dynamical regions in the system and a crossover behavior in the scaling of fluctuations with average.