带噪声的q选民模型中的相变
Phase transitions in the q-voter model with noise on a duplex clique
摘要：
我们研究了一个非线性q-选民模型与随机噪声，解释在社会背景下的独立性，在一个双工网络。为了研究多层次性的作用，我们提出了三种方法将模型从单通道网络转移到多通道网络。它们考虑到两个标准-一个与独立地位有关（独立与全球），一个与同侪压力有关（和与或）。为了研究在社会网络中存在多个级别的影响，我们对一个特别简单的多重-双工集团，它由两个完全重叠的完整图（集团）组成的模拟。数值求解速率方程，同时进行蒙特卡罗模拟，我们提供的证据表明，即使是一个简单的重新排列成一个双工拓扑结构可能会导致显着的变化所观察到的行为。然而，在相变的定性变化可以观察到只有一个所考虑的规则-与和。对于这个规则，当q=5时，相变变得不连续，而对于单重体，当q=6时观察到这种行为。有趣的是，只有这条规则允许构建模型的现实变体，与最近的社会实验一致。
英文摘要：
We study a nonlinear q-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. To study the role of the multi-levelness we propose three methods of transferring the model from a mono- to a multiplex network. They take into account two criteria -- one related to the status of independence (LOCAL vs. GLOBAL) and one related to peer pressure (AND vs. OR). In order to examine the influence of the presence of more than one level in the social network, we perform simulations on a particularly simple multiplex -- a duplex clique, which consists of two fully overlapped complete graphs (cliques). Solving numerically the rate equation and simultaneously conducting Monte Carlo simulations, we provide evidence that even a simple rearrangement into a duplex topology may lead to significant changes in the observed behavior. However, qualitative changes in the phase transitions can be observed for only one of the considered rules -- LOCAL&AND. For this rule the phase transition becomes discontinuous for q=5, whereas for a monoplex such a behavior is observed for q=6. Interestingly, only this rule admits construction of realistic variants of the model, in line with recent social experiments.
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