Exploring complex social contagion, especially the social reinforcement dynamics when exposing to multiple sources , is of vital importance for understanding the spread of complicated collective behaviors nowadays. While previous works exclusively focus on single-layer networks , the detailed impacts of multilayer reinforcement which characterizes the promoting effects among multiple social circles remain largely unknown . To this end, we incorporate multilayer  reinforcement into ignorant-spreader-ignorant (SIS) model on multiplex networks. Our theoretical analysis combines 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.  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 large initial density of adopters with strong multilayer reinforcement. Our results show the powerful and non-negligible impacts of complex dynamical mechanisms, which provides valuable insights toward the spreading behaviors in the digital age .
Social reinforcement mechanism, which characterizes the promoting effects when exposing to multiple sources in social contagion process, is ubiquitous in information-technology ecosystem 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 ignorant-spreader-ignorant (SIS) model on multiplex networks. Our theoretical analysis combines 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 towards 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 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 .
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Exploring complex social contagion, especially the social reinforcement dynamics
Social reinforcement mechanism, which characterizes the promoting effects
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, is of vital importance for understanding the spread of complicated collective behaviors nowadays. While previous works exclusively focus
in social contagion process, is ubiquitous in information-technology ecosystem and has aroused great attention in recent years. While the impacts of social reinforcement
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, the detailed impacts of multilayer reinforcement which characterizes the promoting effects among multiple social circles remain largely unknown
are well-documented, extension to multilayer networks is needed to study how reinforcement from different social circles influences the spreading dynamics
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social
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In particular, the hysteresis loop of stationary prevalence occurs in this bistable region, explaining why the fight towards the spread of rumors is protracted and difficult in modern society.
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show the powerful and
unveil the
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impacts of complex dynamical mechanisms, which provides valuable insights toward the spreading behaviors in the digital age
power of social reinforcement on multiplex networks, which sheds lights on designing efficient strategies in spreading behaviors such as marketing and promoting innovations