  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.
