多路网络上非对称$q$ -选民模型中连续相变的真实生态
A veritable zoology of successive phase transitions in the asymmetric $q$-voter model on multiplex networks
摘要：
我们分析了一个非线性$q$ -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。大厅$q$的大小（即，压力群）是改变系统行为的关键参数。$q$ -表决器模型已被应用于多路复用网络在以前的工作[物理。92. 052812.（2015）]，并且已经表明，相变的特性取决于复用网络中的电平的数量以及$q$的值。在这里，我们研究的情况下，在网络的每一层上的大厅大小是不同的相变特性，导致两个参数$q_1$和$q_2$。我们发现连续的相变的证据时，一个连续的相变之后是一个不连续的一个或两个连续的不连续的阶段出现，这取决于参数。在分析这个系统时，我们甚至会遇到混合阶（或混杂）相变。我们进行模拟，并获得支持一个简单的多重情况下的解析解-一个双工团，它由两个完全重叠的完全图（团）。
英文摘要：
We analyze a nonlinear $q$-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. The size of the lobby $q$ (i.e., the pressure group) is a crucial parameter that changes the behavior of the system. The $q$-voter model has been applied on multiplex networks in a previous work [Phys. Rev E. 92. 052812. (2015)], 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 the value of $q$. Here we study phase transition character in the case when on each level of the network the lobby size is different, resulting in two parameters $q_1$ and $q_2$. We find evidence of successive phase transitions when a continuous phase transition is followed by a discontinuous one or two consecutive discontinuous phases appear, depending on the parameter. When analyzing this system, we even encounter mixed-order (or hybrid) phase transition. We perform simulations and obtain supporting analytical solutions on a simple multiplex case - a duplex clique, which consists of two fully overlapped complete graphs (cliques).
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