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

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 $q\ne 1$ 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 $q\ne 1$. The results are compared with the non-equilibrium phenomena in other well known dynamical systems.

arXiv comment9 pages, 11 figures; new references and text added; some figures changed

References in corpus (43)

• Statistical physics of social dynamics
• Voter Model on Heterogeneous Graphs
• Minority Opinion Spreading in Random Geometry
• Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution
• Incomplete ordering of the voter model on small-world networks
• Coarsening and persistence in the voter model
• Freezing and Slow Evolution in a Constrained Opinion Dynamics Model
• Ordering dynamics with two non-excluding options: Bilingualism in language competition
• Comparison of voter and Glauber ordering dynamics on networks
• Fate of Zero-Temperature Ising Ferromagnets
• Freezing in Ising Ferromagnets
• Disorder induced phase transition in kinetic models of opinion dynamics
• Ultimate Fate of Constrained Voters
• Freezing into Stripe States in Two-Dimensional Ferromagnets and Crossing Probabilities in Critical Percolation
• Role of conviction in nonequilibrium models of opinion formation
• Opinion dynamics in a three-choice system
• Consensus and ordering in language dynamics
• Mean field solutions of kinetic exchange opinion models
• Disorder induced phase transition in an opinion dynamics model: results in 2 and 3 dimensions
• Interface Motion and Pinning in Small World Networks
• Ordering dynamics of the multi-state voter model
• The drastic outcomes from voting alliances in three-party bottom-up democratic voting (1990 $\to$ 2013)
• Phase transition in kinetic exchange opinion models with independence
• Fixation and Polarization in a Three-Species Opinion Dynamics Model
• Exit probability in a one-dimensional nonlinear q-voter model
• Algebraic coarsening in voter models with intermediate states
• On the exit probability of the one dimensional q-voter model. Analytical results and simulations for large networks
• Freezing in random graph ferromagnets
• Irrelevance of information outflow in opinion dynamics models
• Boundary effects in a three-state modified voter model for languages
• Long route to consensus: Two stage coarsening in a binary choice voting model
• Vertex dynamics during domain growth in three-state models
• A stochastic opinion dynamics model with domain size dependent dynamic evolution
• Opinion dynamics model with weighted influence: Exit probability and dynamics
• Exit probability in inflow dynamics: nonuniversality induced by range, asymmetry and fluctuation
• Effect of the nature of randomness on quenching dynamics of Ising model on complex networks
• Interplay of interfacial noise and curvature driven dynamics in two dimensions
• Zero temperature coarsening in Ising model with asymmetric second neighbour interaction in two dimensions
• Absorbing states of zero-temperature Glauber dynamics in random networks
• Exit Probability in Generalised Kinetic Ising Model
• Universal features of exit probability in opinion dynamics models with domain size dependent dynamics
• Minority spin dynamics in non-homogeneous Ising model: diverging timescales and exponents
• Frozen states and active-absorbing phase transitions of the Ising model on networks

Cited by in corpus (2)

• Virtual walks and phase transitions in two dimensional BChS model with extreme switches
• Opinion formation models with extreme switches and disorder: critical behaviour and dynamics