文章基本信息

标题：The Stochastic Transport Dynamics of a Conserved Quantity on a Complex Network
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作者：Pablo Medina ; Jaime Clark ; Miguel Kiwi 等
期刊名称：Scientific Reports
电子版ISSN：2045-2322
出版年度：2018
卷号：8
期号：1
页码：14288
DOI：10.1038/s41598-018-32677-8
语种：English
出版社：Springer Nature
摘要：The stochastic dynamics of conserved quantities is an emergent phenomena observed in many complex systems, ranging from social and to biological networks. Using an extension of the Ehrenfest urn model on a complex network, over which a conserved quantity is transported in a random fashion, we study the dynamics of many elementary packets transported through the network by means of a master equation approach and compare with the mean field approximation and stochastic simulations. By use of the mean field theory, it is possible to compute an approximation to the ensemble average evolution of the number of packets in each node which, in the thermodynamic limit, agrees quite well with the results of the master equation. However, the master equation gives a more complete description of the stochastic system and provides a probabilistic view of the occupation number at each node. Of particular relevance is the standard deviation of the occupation number at each node, which is not uniform for a complex network. We analyze and compare different network topologies (small world, scale free, Erdos-Renyi, among others). Given the computational complexity of directly evaluating the asymptotic, or equilibrium, occupation number probability distribution, we propose a scaling relation with the number of packets in the network, that allows to construct the asymptotic probability distributions from the network with one packet. The approximation, which relies on the same matrix found in the mean field approach, becomes increasingly more accurate for a large number of packets.