Analytical solution of the voter model on uncorrelated networks
Analytical solution of the voter model on uncorrelated networks
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DOI：
10.1088/1367-2630/10/6/063011
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发表时间：
2008-06-09
影响因子：
3.3
通讯作者：
Eguiluz, Victor M.
中科院分区：
文献类型：
--
作者：
Vazquez, Federico;Eguiluz, Victor M.
我们提出了一个数学描述的选民模型动态不相关的网络。当图的平均度为μ 2时，有限系统福尔斯在完全有序化之前，处于准稳态，在准稳态中，存活运行中的活动链接（相反状态节点之间的链接）的平均密度是常数，等于（mu-2）/3（mu-1），而无限大系统则无限地保持在部分有序的稳态活动状态。准稳态的平均寿命与达到全序状态的平均时间T成正比，T的尺度类似于（mu-1）mu N-2/（mu-2）mu（2），其中N是网络的节点数，mu（2）是度分布的二阶矩。我们发现这些分析结果和数值模拟的随机网络与各种程度的分布之间有很好的协议。
We present a mathematical description of the voter model dynamics on uncorrelated networks. When the average degree of the graph is mu 2, a finite system falls, before it fully orders, in a quasi-stationary state in which the average density of active links (links between opposite-state nodes) in surviving runs is constant and equal to (mu-2)/3(mu-1), while an infinitely large system stays ad infinitum in a partially ordered stationary active state. The mean lifetime of the quasi-stationary state is proportional to the mean time to reach the fully ordered state T, which scales as T similar to (mu-1)mu N-2/(mu-2)mu(2) , where N is the number of nodes of the network, and mu(2) is the second moment of the degree distribution. We find good agreement between these analytical results and numerical simulations on random networks with various degree distributions.