The social reinforcement mechanism, which characterizes the promoting effects when exposed to multiple sources in the social contagion process, is ubiquitous in information technology ecosystems and has aroused great attention in recent years. While the impacts of social reinforcement on single-layer networks are well documented, extension to multilayer networks is needed to study how reinforcement from different social circles influences the spreading dynamics. To this end, we incorporate multilayer social reinforcement into an ignorant–spreader–ignorant model on multiplex networks. Our theoretical analysis combines the pairwise method and mean-field theory and agrees well with large-scale simulations. Surprisingly, we find this complex social contagion mechanism triggers the emergence of bistability phenomena, where extinction and outbreak states coexist. In particular, the hysteresis loop of stationary prevalence occurs in this bistable region, explaining why the fight against the spread of rumors is protracted and difficult in modern society. Further, we show that the final state of bistable regions depends on the initial density of adopters, the critical value of which decreases as the contagion transmissibility or the multilayer reinforcement increases. In particular, we highlight two possible conditions for the outbreak of social contagion: to possess large contagion transmissibility, or to possess a large initial density of adopters with strong multilayer reinforcement. Our results unveil the non-negligible power of social reinforcement on multiplex networks, which sheds lights on designing efficient strategies in spreading behaviors such as marketing and promoting innovations.

社会强化机制是在社会传染过程中暴露于多种来源时具有促进作用的特征，在信息技术生态系统中无处不在，近年来引起了广泛关注。虽然社会强化对单层网络的影响有据可查，但需要扩展到多层网络来研究来自不同社交圈的强化如何影响传播动态。为此，我们将多层社会强化纳入多重网络上的无知-传播者-无知模型。我们的理论分析结合了成对方法和平均场理论，并且与大规模模拟非常吻合。令人惊讶的是，我们发现这种复杂的社会传染机制引发了双稳态现象的出现，灭绝和爆发状态共存的地方。尤其是在这个双稳态区域发生了平稳流行的滞后环，这解释了为什么现代社会打击谣言传播的斗争旷日持久。此外，我们表明双稳态区域的最终状态取决于采用者的初始密度，其临界值随着传染性或多层增强的增加而降低。我们特别强调了社会传染爆发的两种可能条件：具有大的传染性，或具有强大的多层强化的初始采用者密度大。我们的结果揭示了多重网络上社会强化的不可忽视的力量，