In a recent work [Shao $et$ $al$ 2009 Phys. Rev. Lett. \textbf{108} 018701], a nonconsensus opinion (NCO) model was proposed, where two opinions can stably coexist by forming clusters of agents holding the same opinion. The NCO model on lattices and several complex networks displays a phase transition behavior, which is characterized by a large spanning cluster of nodes holding the same opinion appears when the initial fraction of nodes holding this opinion is above a certain critical value. In the NCO model, each agent will convert to its opposite opinion if there are more than half of agents holding the opposite opinion in its neighborhood. In this paper, we generalize the NCO model by assuming that each agent will change its opinion if the fraction of agents holding the opposite opinion in its neighborhood exceeds a threshold $T$ ($T\geq 0.5$). We call this generalized model as the NCOT model. We apply the NCOT model on different network structures and study the formation of opinion clusters. We find that the NCOT model on lattices displays a continuous phase transition. For random graphs and scale-free networks, the NCOT model shows a discontinuous phase transition when the threshold is small and the average degree of the network is large, while in other cases the NCOT model displays a continuous phase transition.
本文研究了正方格子LCCC模型（Lallouache et al. in Phys. Rev. E 82 056112（2010）中提出的一种观点交换动力学模型）中几何团簇随信念和影响参数变化的逾渗转变.所述聚类包括具有大于或等于意见的预定阈值（Ω）的意见值的相邻站点。该转变点与Lallouache等人发现的序参量（平均意见值）的转变点不同。虽然转变点随意见阈值的变化而变化，但从最大团簇尺寸、团簇尺寸分布和Binder累积量的数据崩溃中获得的逾渗转变的临界指数保持不变。的指数也是独立的信念和影响参数的值，表明这种过渡的鲁棒性。这些指数与任何其他已知的渗透指数（例如静态伊辛、动态伊辛、标准渗透）不匹配，因此表征了LCCC模型属于单独的普适类。
Probabilistic neighbors' selection competes with confirmation bias in a bounded confidence model
CNRS, Complex Systems Institute of Paris Île-de-France (ISC-PIF)（法国国家科学研究中心，巴黎法兰西岛复杂系统研究所）；Laboratoire de Physique Théorique et Modélisation, CNRS-CY Cergy Paris Université（理论与建模物理实验室，CNRS-CY塞尔吉巴黎大学）；EHESS, Centre d’Analyse et de Mathématique Sociales (CAMS)（高等社会科学学院，社会分析与数学中心）；Cergy Paris Université（塞尔吉巴黎大学）
