Chmiel Anna, Sienkiewicz Julian, Fronczak Agata, Fronczak Piotr
Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.
Entropy (Basel). 2020 Sep 11;22(9):1018. doi: 10.3390/e22091018.
We analyze a nonlinear -voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. The size of the lobby (i.e., the pressure group) is a crucial parameter that changes the behavior of the system. The -voter model has been applied on multiplex networks, and it has been shown that the character of the phase transition depends on the number of levels in the multiplex network as well as on the value of . The primary aim of this study is to examine phase transition character in the case when on each level of the network the lobby size is different, resulting in two parameters q1 and q2. In a system of a duplex clique (i.e., two fully overlapped complete graphs) we find evidence of successive phase transitions when a continuous phase transition is followed by a discontinuous one or two consecutive discontinuous phase transitions appear, depending on the parameter. When analyzing this system, we even encounter mixed-order (or hybrid) phase transition. The observation of successive phase transitions is a new quantity in binary state opinion formation models and we show that our analytical considerations are fully supported by Monte-Carlo simulations.
我们分析了一个具有随机噪声的非线性选民模型，在社会背景下将其解释为独立性，该模型应用于双工网络。游说团体（即压力集团）的规模是一个关键参数，它会改变系统的行为。选民模型已应用于多重网络，并且已经表明相变的特征取决于多重网络中的层数以及 的值。本研究的主要目的是考察当网络的每个层级上的游说团体规模不同时的相变特征，这会产生两个参数q1和q2。在双工团簇系统（即两个完全重叠的完全图）中，我们发现存在连续相变的证据，即先是连续相变，接着是不连续相变，或者出现两个连续的不连续相变，这取决于参数。在分析这个系统时，我们甚至遇到了混合序（或混合）相变。连续相变的观测在二元状态意见形成模型中是一个新现象，并且我们表明我们的分析性考量得到了蒙特卡罗模拟的充分支持。
