Nonequilibrium dynamics in a three-state opinion-formation model with stochastic extreme switches

We investigate the nonequilibrium dynamics of a three-state kinetic exchange model of opinion formation, where switches between extreme states are possible, depending on the value of a parameter q. The mean field dynamical equations are derived and analyzed for any q. The fate of the system under the evolutionary rules used in S. Biswas et al. [Physica A 391, 3257 (2012)] shows that it is dependent on the value of q and the initial state in general. For q = 1, which allows the extreme switches maximally, a quasiconservation in the dynamics is obtained which renders it equivalent to the voter model. For general q values, a "frozen" disordered fixed point is obtained which acts as an attractor for all initially disordered states. For other initial states, the order parameter grows with time t as exp[alpha(q)t] where alpha = 1-q/3-q for q not equal 1 and follows a power law behavior for q = 1. Numerical simulations using a fully connected agent-based model provide additional results like the system size dependence of the exit probability and consensus times that further accentuate the different behavior of the model for q = 1 and q not equal 1. The results are compared with the nonequilibrium phenomena in other well-known dynamical systems.