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

TL;DR

This paper studies a three-state opinion formation model with stochastic extreme switches, analyzing its non-equilibrium dynamics, fixed points, and how the parameter q influences system behavior, including consensus formation.

Contribution

The paper derives and analyzes mean field dynamical equations for the model across all q values, revealing distinct behaviors at q=1 and q≠1, and provides numerical simulations to support these findings.

Findings

At q=1, the model behaves like the voter model with power-law dynamics.

For q≠1, the system reaches a frozen disordered fixed point.

Numerical results show different consensus times and exit probabilities depending on q.

Abstract

We investigate the non-equilibrium 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 analysed for any $q$. The fate of the system under the evolutionary rules used in \cite{BCS} 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 quasi-conservation 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 $\alpha = \frac{1-q}{3-q}$ for $q\neq 1$ and follows a power law behaviour 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 behaviour of the model for $q=1$ and $q\neq 1$. The results are compared with the non-equilibrium phenomena in other well known dynamical systems.