标题： 阈值$q$投票模型 显示英文标题

标题： Threshold $q$-voter model

摘要： We introduce the threshold $q$-voter opinion dynamics where an agent, facing a binary choice, can change its mind when at least $q_0$ amongst $q$ neighbors share the opposite opinion. Otherwise, the agent can still change its mind with a certain probability $\varepsilon$. This threshold dynamics contemplates the possibility of persuasion by an influence group even when there is not full agreement among its members. 事实上，个体不仅在游说团体中存在一致意见（$q_0=q$）时会跟随其同伴，如$q$投票者模型所假设的那样，而且根据具体情况，当存在简单多数（$q_0>q/2$）、拜占庭共识（$q_0>2q/3$）或任何最小数量（$q_0$）在$q$之中时也会这样做。 这种现实的阈值导致了出现集体状态和相变，这些在标准的$q$投票者中未被观察到。 阈值$q_0$，以及由$\varepsilon$引入的随机性，产生了一种现象学，它将$q$-投票者与非一致性及独立性等随机驱动作为特例。特别是，非共识的多数状态是可能的，以及混合相。连续和不连续的相变可能发生，但也可以从波动相转变为吸收态。 显示英文摘要

摘要： We introduce the threshold $q$-voter opinion dynamics where an agent, facing a binary choice, can change its mind when at least $q_0$ amongst $q$ neighbors share the opposite opinion. Otherwise, the agent can still change its mind with a certain probability $\varepsilon$. This threshold dynamics contemplates the possibility of persuasion by an influence group even when there is not full agreement among its members. In fact, individuals can follow their peers not only when there is unanimity ($q_0=q$) in the lobby group, as assumed in the $q$-voter model, but, depending on the circumstances, also when there is simple majority ($q_0>q/2$), Byzantine consensus ($q_0>2q/3$), or any minimal number $q_0$ amongst $q$. This realistic threshold gives place to emerging collective states and phase transitions which are not observed in the standard $q$-voter. The threshold $q_0$, together with the stochasticity introduced by $\varepsilon$, yields a phenomenology that mimics as particular cases the $q$-voter with stochastic drivings such as nonconformity and independence. In particular, nonconsensus majority states are possible, as well as mixed phases. Continuous and discontinuous phase transitions can occur, but also transitions from fluctuating phases into absorbing states.