Abstract
We investigate mean-field dynamics of a nonlinear opinion formation model with congregator and contrarian agents. Each agent assumes one of the two possible states. Congregators imitate the state of other agents with a rate that increases with the number of other agents in the opposite state, as in the linear voter model and nonlinear majority voting models. Contrarians flip the state with a rate that increases with the number of other agents in the same state. The nonlinearity controls the strength of the majority voting and is used as a main bifurcation parameter. We show that the model undergoes a rich bifurcation scenario comprising the egalitarian equilibrium, two symmetric lopsided equilibria, limit cycle, and coexistence of different types of stable equilibria with intertwining attractive basins.
Highlights
In real society, pure consensus seems to be an exception rather than a norm.12 In meanfield populations, idiosyncratic preferences of individuals13–16 and contrarians6–9,11,17–20 are among two driving forces to prevent consensus
We show that the model undergoes a rich bifurcation scenario comprising the egalitarian equilibrium, two symmetric lopsided equilibria, limit cycle, and coexistence of different types of stable equilibria with intertwining attractive basins
We mainly investigate the bifurcation scenario of the mean-field dynamics of this agent-based model, where the nonlinearity with which an agent complies with the majority voting is taken as a chief bifurcation parameter
Summary
In real society, pure consensus seems to be an exception rather than a norm. In meanfield populations, idiosyncratic preferences of individuals and contrarians are among two driving forces to prevent consensus. We examine effects of contrarian agents in a nonlinear opinion formation model. Nonlinear opinion formation models with contrarians have been shown to exhibit phase transition between a consensus-like phase and an egalitarian phase.. A complementary dynamical approach to opinion formation with contrarian agents was recently made with the use of coupled Kuramoto oscillators with contrarian oscillators.21–23 Agents in these studies are implicitly assumed to be intrinsic oscillators. We investigate the equilibria and dynamics of a continuous-time nonlinear voter model with contrarian agents. We extend an agent-based linear voter model with contrarians proposed in Ref. 20 by introducing nonlinear interaction. With d 1⁄4 1, the conversion rate is proportional to the number of agents in the opposite state, as is the case for the voter model. Equations (1) and (2) are invariant under the transformation ðx; yÞ ! ðX À x; Y À yÞ, reflecting the symmetry between the two states
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