Multilayer social reinforcement induces bistability on multiplex networks

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.