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We study an asymmetric version of the threshold model with anticonformityunder asynchronous update mode that mimics continuous time. We study this modelon a complete graph using three different approaches: mean-field approximation,Monte Carlo simulation, and the Markov chain approach. The latter approachyields analytical results for arbitrarily small systems, in contrast to themean-field approach, which is strictly correct only for an infinite system. Weshow that for sufficiently large systems, all three approaches produce the sameresults, as expected. We consider two cases: (1) homogeneous, in which allagents have the same tolerance threshold, and (2) heterogeneous, in which thethresholds are given by a beta distribution parametrized by two positive shapeparameters $\alpha$ and $\beta$. The heterogeneous case can be treated as ageneralized model that reduces to a homogeneous model in special cases. We showthat particularly interesting behaviors, including social hysteresis andcritical mass, arise only for values of $\alpha$ and $\beta$ that yield theshape of the distribution observed in real social systems.

The threshold model with anticonformity under random sequential updating