随机序贯更新下具有反整合的门限模型
The threshold model with anticonformity under random sequential updating
摘要：
本文研究了在模拟连续时间的异步更新模式下具有反整合的非对称阈值模型。我们使用三种不同的方法：平均场近似，蒙特卡罗模拟，和马尔可夫链方法研究这个模型上的一个完整的图。后一种方法产生的任意小系统的分析结果，在平均场的方法，这是严格正确的，只有一个无限大的系统。我们表明，对于足够大的系统，所有三种方法产生相同的结果，正如预期的那样。我们考虑两种情况：（1）均质，其中所有代理具有相同的容忍阈值，以及（2）异质，其中阈值由两个正形状参数$α$和$β$参数化的β分布给出。异质情况可以被视为一个广义模型，在特殊情况下，减少到一个同质的模型。我们发现，特别有趣的行为，包括社会滞后和临界质量，只出现值的$α$和$β$，产生的形状的分布在现实的社会系统。
英文摘要：
We study an asymmetric version of the threshold model with anticonformity under asynchronous update mode that mimics continuous time. We study this model on a complete graph using three different approaches: mean-field approximation, Monte Carlo simulation, and the Markov chain approach. The latter approach yields analytical results for arbitrarily small systems, in contrast to the mean-field approach, which is strictly correct only for an infinite system. We show that for sufficiently large systems, all three approaches produce the same results, as expected. We consider two cases: (1) homogeneous, in which all agents have the same tolerance threshold, and (2) heterogeneous, in which the thresholds are given by a beta distribution parametrized by two positive shape parameters $α$ and $β$. The heterogeneous case can be treated as a generalized model that reduces to a homogeneous model in special cases. We show that particularly interesting behaviors, including social hysteresis and critical mass, arise only for values of $α$ and $β$ that yield the shape of the distribution observed in real social systems.
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