Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany.
Department of Physics, Humboldt University, Newtonstrasse 15, 12489 Berlin, Germany.
Phys Rev E. 2017 Nov;96(5-1):052315. doi: 10.1103/PhysRevE.96.052315. Epub 2017 Nov 28.
The adaptive voter model has been widely studied as a conceptual model for opinion formation processes on time-evolving social networks. Past studies on the effect of zealots, i.e., nodes aiming to spread their fixed opinion throughout the system, only considered the voter model on a static network. Here we extend the study of zealotry to the case of an adaptive network topology co-evolving with the state of the nodes and investigate opinion spreading induced by zealots depending on their initial density and connectedness. Numerical simulations reveal that below the fragmentation threshold a low density of zealots is sufficient to spread their opinion to the whole network. Beyond the transition point, zealots must exhibit an increased degree as compared to ordinary nodes for an efficient spreading of their opinion. We verify the numerical findings using a mean-field approximation of the model yielding a low-dimensional set of coupled ordinary differential equations. Our results imply that the spreading of the zealots' opinion in the adaptive voter model is strongly dependent on the link rewiring probability and the average degree of normal nodes in comparison with that of the zealots. In order to avoid a complete dominance of the zealots' opinion, there are two possible strategies for the remaining nodes: adjusting the probability of rewiring and/or the number of connections with other nodes, respectively.
自适应投票模型已被广泛研究为随时间演变的社交网络上意见形成过程的概念模型。过去关于狂热分子（即旨在在整个系统中传播其固定意见的节点）影响的研究仅考虑了静态网络上的投票模型。在这里，我们将狂热主义的研究扩展到节点状态与自适应网络拓扑共同演变的情况，并根据狂热分子的初始密度和连通性研究由狂热分子引起的意见传播。数值模拟表明，在碎片化阈值以下，少量的狂热分子就足以将其意见传播到整个网络。在过渡点之后，狂热分子必须比普通节点具有更高的度数，才能有效地传播其意见。我们使用模型的平均场逼近来验证数值结果，得到一组低维耦合常微分方程。我们的结果表明，与狂热分子相比，自适应投票模型中狂热分子意见的传播强烈依赖于链路重连概率和普通节点的平均度数。为了避免狂热分子意见的完全主导地位，其余节点有两种可能的策略：分别调整重连概率和/或与其他节点的连接数。
