Characterization of the nonequilibrium steady state of a heterogeneous nonlinear q-voter model with zealotry

被引:34
|
作者
Mellor, Andrew [1 ]
Mobilia, Mauro [1 ]
Zia, R. K. P. [2 ,3 ]
机构
[1] Univ Leeds, Sch Math, Dept Appl Math, Leeds LS2 9JT, W Yorkshire, England
[2] Iowa State Univ, Dept Phys & Astron, Ames, IA 50011 USA
[3] Virginia Polytech Inst & State Univ, Dept Phys, Blacksburg, VA 24061 USA
基金
美国国家科学基金会; 英国工程与自然科学研究理事会;
关键词
OPINION DYNAMICS; SYSTEMS;
D O I
10.1209/0295-5075/113/48001
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We introduce a heterogeneous nonlinear q-voter model with zealots and two types of susceptible voters, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a zealot or a susceptible voter of type q(1) or q(2). While here zealots never change their opinion, a q(i)-susceptible voter (i = 1, 2) consults a group of q(i) neighbors at each time step, and adopts their opinion if all group members agree. We show that this model violates the detailed balance whenever q(1) not equal q(2) and has surprisingly rich properties. Here, we focus on the characterization of the model's non-equilibrium stationary state (NESS) in terms of its probability distribution and currents in the distinct regimes of low and high density of zealotry. We unveil the NESS properties in each of these phases by computing the opinion distribution and the circulation of probability currents, as well as the two-point correlation functions at unequal times (formally related to a "probability angular momentum"). Our analytical calculations obtained in the realm of a linear Gaussian approximation are compared with numerical results. Copyright (C) EPLA, 2016
引用
收藏
页数:6
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