论文标题
多国家选民模型中的本地和全球秩序动态
Local and global ordering dynamics in multi-state voter models
论文作者
论文摘要
我们研究了主动链接密度的时间演变以及具有全面互动和不相关网络的多状态选民模型中观点之间分布的熵的时间演变。个人的实现会经历一系列消除意见，直到达成共识为止。每次消除后，人口保持元稳定状态。活动链接的密度和这些状态中的熵因实现而异。做出一些简单的假设，我们能够分析计算活动链接的平均密度和这些状态中的平均熵。我们还表明，在实现上平均，主动链接的密度呈指数衰减，按时间尺度设置为图表的大小和几何形状，但独立于最初的意见状态。平均熵的衰减只有在人口中最多有两个意见的时间长时间才达成指数。最后，我们展示了如何通过在每种现有意见中精确地引入一个狂热的狂热者来人为地设计的元稳定状态可以人为地设计。
We investigate the time evolution of the density of active links and of the entropy of the distribution of agents among opinions in multi-state voter models with all-to-all interaction and on uncorrelated networks. Individual realisations undergo a sequence of eliminations of opinions until consensus is reached. After each elimination the population remains in a meta-stable state. The density of active links and the entropy in these states varies from realisation to realisation. Making some simple assumptions we are able to analytically calculate the average density of active links and the average entropy in each of these states. We also show that, averaged over realisations, the density of active links decays exponentially, with a time scale set by the size and geometry of the graph, but independent of the initial number of opinion states. The decay of the average entropy is exponential only at long times when there are at most two opinions left in the population. Finally, we show how meta-stable states comprised of only a subset of opinions can be artificially engineered by introducing precisely one zealot in each of the prevailing opinions.
