We introduce a three-state model to study the effects of a neutral party on opinion spreading, in which the tendency of agents to agree with their neighbors can be tuned to favor either the neutral party or two oppositely polarized parties, and can be disrupted by social agitation mimicked as temperature. We study the equilibrium phase diagram and the non-equilibrium stochastic dynamics of the model with various analytical approaches and with Monte Carlo simulations on different substrates: the fully-connected (FC) graph, the one-dimensional (1D) chain, and Erdös-Rényi (ER) random graphs. We show that, in the mean-field approximation, the phase boundary between the disordered and polarized phases is characterized by a tricritical point. On the FC graph, in the absence of social agitation, kinetic barriers prevent the system from reaching optimal consensus. On the 1D chain, the main result is that the dynamics is governed by the growth of opinion clusters. Finally, for the ER ensemble a phase transition analogous to that of the FC graph takes place, but now the system is able to reach optimal consensus at low temperatures, except when the average connectivity is low, in which case dynamical traps arise from local frozen configurations.
Mean field solutions of kinetic exchange opinion models
在这里，我们提出了一个无限范围，离散，意见形成模型的精确解。该模型显示出主动吸收相变，类似于在其最近提出的连续版本（Lallouache等人，Rev E 82，056112（2010））。除了两个代理人的相互作用，我们还报告了有三个代理人的相互作用的影响。该相图具有由三临界点分开的连续过渡线（两种试剂相互作用为主）和不连续过渡线（三种试剂相互作用为主）。
Fixation and Polarization in a Three-Species Opinion Dynamics Model
受文化变化和多样性的动力学的启发，我们在[J. Phys. A 37，8479（2004）]中引入的完全图上推广了三种群约束投票模型。在这个观点动力学模型中，规模为N的人口由“左派”和“右派”组成，他们与“中间派”互动：左派和中间派都可以成为比率为（1+q）/2的左派或比率为（1-q）/2的中间派（右派和中间派也是如此），其中q表示对极端主义（q>0）或中间主义（q<0）的偏见。这一体系承认三个吸引人的固定点和一条“极化”线，沿着这条线，左派和右派的混合物冻结共存。在Fokker-Planck方程的范畴内，通过对种群遗传学模型的映射，计算了在每个吸收态结束的固定概率和这些事件的平均时间。因此，我们显示，特别是在弱的偏见和大的人口规模的限制时，|q| ~1/N和N>>1，波动如何改变平均场的预测：极化是可能的，当q>0，但总是有一个有限的概率达到共识，相反的情况下，当q<0。我们的研究结果证实了随机模拟。
