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We study the dynamics of the out-of-equilibrium nonlinear q-voter model withtwo types of susceptible voters and zealots, introduced in [EPL 113, 48001(2016)]. In this model, each individual supports one of two parties and iseither 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, whilezealots are inflexible and never change their opinion. This model violatesdetailed balance whenever $q_1 \neq q_2$ and is characterized by two distinctregimes of low and high density of zealotry. Here, by combining analytical andnumerical methods, we investigate the non-equilibrium stationary state of thesystem in terms of its probability distribution, non-vanishing currents andunequal-time two-point correlation functions. We also study the switching timesproperties of the model by exploiting an approximate mapping onto the model of[Phys. Rev. E 92, 012803 (2015)] that satisfies the detailed balance, and alsooutline some properties of the model near criticality.

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