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

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 $q_1\ne q_2$ 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.

17 pages, 12 figures

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Cited by in corpus (10)

• Zealots in the mean-field noisy voter model
• Distribution of the time of the maximum for stationary processes
• Homogeneous symmetrical threshold model with nonconformity: independence vs. anticonformity
• Zealots in multi-state noisy voter models
• Polarization and Consensus in a Voter Model under Time-Fluctuating Influences
• Nonequilibrium oscillations, probability angular momentum, and the climate system
• How does homophily shape the topology of a dynamic network?
• Effects of homophily and heterophily on preferred-degree networks: mean-field analysis and overwhelming transition
• Breaking coexistence: Zealotry vs. nonlinear social impact
• When heterogeneity drives hysteresis: Anticonformity in the multistate $q$-voter model on networks