  The threshold model has been widely adopted as a classic model for studying
contagion processes on social networks. We consider asymmetric individual
interactions in social networks and introduce a persuasion mechanism into the
threshold model. Specifically, we study a combination of adoption and
persuasion in cascading processes on complex networks. It is found that with
the introduction of the persuasion mechanism, the system may become more
vulnerable to global cascades, and the effects of persuasion tend to be more
significant in heterogeneous networks than those in homogeneous networks: a
comparison between heterogeneous and homogeneous networks shows that under weak
persuasion, heterogeneous networks tend to be more robust against random shocks
than homogeneous networks; whereas under strong persuasion, homogeneous
networks are more stable. Finally, we study the effects of adoption and
persuasion threshold heterogeneity on systemic stability. Though both
heterogeneities give rise to global cascades, the adoption heterogeneity has an
overwhelmingly stronger impact than the persuasion heterogeneity when the
network connectivity is sufficiently dense.
