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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.
A theory of symbolic dynamic systems with long-range correlations based on the consideration of the binary N-step Markov chains developed earlier in Phys. Rev. Lett. 90, 110601 (2003) is generalized to the biased case (non equal numbers of zeros and
We investigate the time evolution of the scores of the second most popular sport in world: the game of cricket. By analyzing the scores event-by-event of more than two thousand matches, we point out that the score dynamics is an anomalous diffusive p
To provide a more accurate description of the driving behaviors in vehicle queues, a namely Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process whose stat
It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting numbers. We
Many complex systems, including networks, are not static but can display strong fluctuations at various time scales. Characterizing the dynamics in complex networks is thus of the utmost importance in the understanding of these networks and of the dy