Nonlinear $q$-voter model with inflexible zealots

Abstract

We study the dynamics of the nonlinear $q$-voter model with inflexible zealots in a finite well-mixed population. In this system, each individual supports one of two parties and is either a susceptible voter or an inflexible zealot. At each time step, a susceptible adopts the opinion of a neighbor if this belongs to a group of $q\ge 2$ neighbors all in the same state, whereas inflexible zealots never change their opinion. In the presence of zealots of both parties the model is characterized by a fluctuating stationary state and, below a zealotry density threshold, the distribution of opinions is bimodal. After a characteristic time, most susceptibles become supporters of the party having more zealots and the opinion distribution is asymmetric. When the number of zealots of both parties is the same, the opinion distribution is symmetric and, in the long run, susceptibles endlessly swing from the state where they all support one party to the opposite state. Above the zealotry density threshold, when there is an unequal number of zealots of each type, the probability distribution is single-peaked and non-Gaussian. These properties are investigated analytically and with stochastic simulations. We also study the mean time to reach a consensus when zealots support only one party.

11 pages, 10 figures. For Physical Review E (accepted, final version)

References in corpus (14)

• Statistical physics of social dynamics
• Does a Single Zealot Affect an Infinite Group of Voters ?
• On the Role of Zealotry in the Voter Model
• The role of inflexible minorities in the breaking of democratic opinion dynamics
• Analytical results for the Sznajd model of opinion formation
• Dynamics of Non-Conservative Voters
• Opinion control in complex networks
• Voting and Catalytic Processes with Inhomogeneities
• Evolution of cooperation driven by zealots
• Some new results on one-dimensional outflow dynamics
• Stochastic dynamics of the prisoner's dilemma with cooperation facilitators
• Commitment versus persuasion in the three-party constrained voter model
• Fixation of a Deleterious Allele under Mutation Pressure and Finite Selection Intensity
• Coexistence in neutral theories: interplay of criticality and mild local preferences

Cited by in corpus (15)

• Zealots in the mean-field noisy voter model
• A Heterogeneous Out-of-Equilibrium Nonlinear $q$-Voter Model with Zealotry
• Homogeneous symmetrical threshold model with nonconformity: independence vs. anticonformity
• Polarization and Consensus in a Voter Model under Time-Fluctuating Influences
• Role of inflexible minorities in the evolution of alcohol consumption
• 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
• Nonequilibrium phase transitions and absorbing states in a model for the dynamics of religious affiliation
• Discerning media bias within a network of political allies and opponents: Disruption by partisans
• Shannon information criterion for low-high diversity transition in Moran and Voter models
• Breaking coexistence: Zealotry vs. nonlinear social impact
• When heterogeneity drives hysteresis: Anticonformity in the multistate $q$-voter model on networks
• The role of zealots in the spread of linguistic traits
• Coevolutionary Dynamics of Group Interactions: Coevolving Nonlinear Voter Models
• Competition between private and expressed opinions in binary choice: the $\alpha$-EPO $q$-voter model