Stationary concentrations of opinions as a function of independence probability p.

Concentrations of positive public opinions are presented in upper panels (a)-(c), whereas concentrations of positive private opinions are presented in bottom panels (d)-(f). Different columns correspond to different q-panel sizes: (a) and (d) q = 4, (b) and (e) q = 5, and (c) and (f) q = 6. Analytical results are represented by lines, solid for stable states and dotted for unstable ones: gray lines stand for AT and TA models, whereas black lines, which do not overlap symbols, stand for the original q-voter model with independence [2]. In general, transition points for the original q-voter model are located in the area of smaller values of independence than in the case of AT and TA models. Symbols represent results of Monte Carlo simulations with ordered initial conditions (S_i(0) = σ_i(0) = 1 for all agents): △ for TA (think then act) and • for AT (act then think) models. It is seen that TA and AT models give exactly the same outcomes. Moreover, for q ≥ 5, the metastable region, where both order and disordered phases are stable, and they coexist, shows up. Results from Monte Carlo simulations have been obtained for the system of the size N = 10⁵ averaged over 100 samples after 10⁵ MCS.