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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 pc such that for a weak external field (p<pc), 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>pc), 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 quasistationary distribution and is found to be in agreement with the results obtained by numerical simulations.
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Singh et al. (2016) studied this question.
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