Abstract In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $\langle F_i \rangle$ of the $i$-th node and its variance $\sigma_i$ as $\sigma_i \propto \langle F_{i} \rangle ^ {\alpha}$. Such scaling laws are found to be prevalent both in natural and man-made network systems, but the understanding of their origins still remains limited. This paper proposes a non-stationary Poisson process model 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 behaviour 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.
Received: 30 October 2008
Revised: 14 November 2008
Accepted manuscript online:
Fund: Project supported in
part by National Basic Research Program of China (973 Project)
(Grant No 2006CB705506), Hi-Tech Research and Development Program of
China (863 Project) (Grant No 2007AA11Z222), National Natural
Science Foundation of China (Grant Nos 6
Cite this article:
Chen Yu-Dong(陈煜东), Li Li(李力), Zhang Yi(张毅), and Hu Jian-Ming(胡坚明) Fluctuations and pseudo long range dependence in network flows: A non-stationary Poisson process model 2009 Chin. Phys. B 18 1373
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