Competing Effects of Social Balance and Influence

We study a three-state (leftist, rightist, centrist) model that couples the dynamics of social balance with an external deradicalizing field. The mean-field analysis shows that there exists a critical value of the external field $p_c$ such that for a weak external field ($p$$<$$p_c$), the system exhibits a metastable fixed point and a saddle point in addition to a stable fixed point. However, if the strength of the external field is sufficiently large ($p$$>$$p_c$), there is only one (stable) fixed point which corresponds to an all-centrist consensus state (absorbing state). In the weak-field regime, the convergence time to the absorbing state is evaluated using the quasi-stationary distribution and is found to be in agreement with the results obtained by numerical simulations.