Shi Feng, Mucha Peter J, Durrett Richard
Department of Mathematics, CB No. 3250, University of North Carolina, Chapel Hill, North Carolina 27599-3250, USA.
Department of Mathematics, Box 90320, Duke University, Durham, North Carolina 27708-0320, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Dec;88(6):062818. doi: 10.1103/PhysRevE.88.062818. Epub 2013 Dec 30.
We consider an idealized model in which individuals' changing opinions and their social network coevolve, with disagreements between neighbors in the network resolved either through one imitating the opinion of the other or by reassignment of the discordant edge. Specifically, an interaction between x and one of its neighbors y leads to x imitating y with probability (1-α) and otherwise (i.e., with probability α) x cutting its tie to y in order to instead connect to a randomly chosen individual. Building on previous work about the two-opinion case, we study the multiple-opinion situation, finding that the model has infinitely many phase transitions (in the large graph limit with infinitely many initial opinions). Moreover, the formulas describing the end states of these processes are remarkably simple when expressed as a function of β=α/(1-α).
我们考虑一个理想化模型，其中个体不断变化的观点及其社会网络共同演化，网络中邻居之间的分歧通过一方模仿另一方的观点或通过重新分配不一致的边来解决。具体而言，x与其邻居y之一之间的交互导致x以概率(1-α)模仿y，否则（即概率为α）x切断与y的联系，转而连接到随机选择的个体。基于先前关于双观点情况的研究，我们研究了多观点情况，发现该模型有无限多个相变（在具有无限多个初始观点的大图极限中）。此外，当表示为β=α/(1-α)的函数时，描述这些过程最终状态的公式非常简单。
