Voter models on heterogeneous networks
Voter models on heterogeneous networks
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DOI：
10.1103/physreve.77.041121
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发表时间：
2008-04-01
影响因子：
2.4
通讯作者：
Redner, S.
中科院分区：
文献类型：
--
作者：
Sood, V.;Antal, Tibor;Redner, S.
我们研究了异构网络上的简单相互作用粒子系统，包括投票模型和入侵过程。这两种模型都是两状态模型，在更新事件中，个体改变状态以与邻居达成一致。对于选民模型，一个人从随机选择的邻居“导入”其状态。这里，对于具有不相关度分布的N个节点的网络，达到共识的平均时间T-N为N mu（2）（1）/mu（2），其中mu（k）是度分布的第k阶矩。因此，在具有广泛度分布的网络上，迅速达成共识。我们还确定了守恒定律，其特点是达成共识的路线。并行结果来自入侵过程中，代理的状态是“出口”到一个随机的邻居。我们进一步推广到偏置动力学，其中一个状态是有利的。一个单一的fitter突变体位于节点的度k覆盖人口的固定概率是成比例的选民模型的k和1/k的入侵过程。
We study simple interacting particle systems on heterogeneous networks, including the voter model and the invasion process. These are both two-state models in which in an update event an individual changes state to agree with a neighbor. For the voter model, an individual "imports" its state from a randomly chosen neighbor. Here the average time T-N to reach consensus for a network of N nodes with an uncorrelated degree distribution scales as N mu(2)(1)/mu(2), where mu(k) is the kth moment of the degree distribution. Quick consensus thus arises on networks with broad degree distributions. We also identify the conservation law that characterizes the route by which consensus is reached. Parallel results are derived for the invasion process, in which the state of an agent is "exported" to a random neighbor. We further generalize to biased dynamics in which one state is favored. The probability for a single fitter mutant located at a node of degree k to overspread the population-the fixation probability-is proportional to k for the voter model and to 1/k for the invasion process.