A Heterogeneous Out-of-Equilibrium Nonlinear $q$-Voter Model with Zealotry

TL;DR

This paper analyzes a complex opinion dynamics model involving susceptible voters and zealots, revealing non-equilibrium behaviors, phase regimes, and critical properties through combined analytical and numerical approaches.

Contribution

It introduces a detailed study of a nonlinear q-voter model with zealots, highlighting non-equilibrium stationary states and switching dynamics in regimes with different zealotry densities.

Findings

Identification of non-equilibrium stationary distributions

Analysis of probability currents and correlations

Characterization of switching times and critical behavior

Abstract

We study the dynamics of the out-of-equilibrium nonlinear q-voter model with two types of susceptible voters and zealots, introduced in [EPL 113, 48001 (2016)]. In this model, each individual supports one of two parties and is either a susceptible voter of type $q_1$ or $q_2$, or is an inflexible zealot. At each time step, a $q_i$-susceptible voter ($i = 1,2$) consults a group of $q_i$ neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. This model violates detailed balance whenever $q_1 \neq q_2$ and is characterized by two distinct regimes of low and high density of zealotry. Here, by combining analytical and numerical methods, we investigate the non-equilibrium stationary state of the system in terms of its probability distribution, non-vanishing currents and unequal-time two-point correlation functions. We also study the switching times properties of the model by exploiting an approximate mapping onto the model of [Phys. Rev. E 92, 012803 (2015)] that satisfies the detailed balance, and also outline some properties of the model near criticality.