  In the study of complex networks (systems), the scaling phenomenon of flow
fluctuations refers to a certain power-law between the mean flux (activity)
$<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto <
F_{i} > ^{\alpha}$. Such scaling laws are found to be prevalent both in natural
and man-made network systems, but our understanding of their origins still
remains limited. In this paper, a non-stationary Poisson process model is
proposed to give an analytical explanation of the non-universal scaling
phenomenon: the exponent $\alpha$ varies between 1/2 and 1 depending on the
size of sampling time window and the relative strength of the external/internal
driven forces of the systems. The crossover behavior and the relation of
fluctuation scaling with pseudo long range dependence are also accounted for by
the model. Numerical experiments show that the proposed model can recover the
multi-scaling phenomenon.
