Dynamics of social contagions with heterogeneous adoption thresholds: crossover phenomena in phase transition

Heterogeneous adoption thresholds exist widely in social contagions, such as behavior spreading, but were always neglected in previous studies. To this end, we introduce heterogeneous adoption threshold distribution into a non-Markovian spreading threshold model, in which an individual adopts a behavior only when the received cumulative pieces of behavioral information from neighbors exceeds his adoption threshold. In order to understand the effects of heterogeneous adoption thresholds quantitatively, an edge-based compartmental theory is developed. Atwo-state spreading threshold model is taken as an example, in which some individuals have a low adoption threshold (i.e., activists) while the remaining ones hold a relatively higher adoption threshold (i.e., bigots). We find a hierarchical characteristic in adopting behavior, i.e., activists first adopt the behavior and then stimulate bigots to adopt the behavior. Interestingly, two types of crossover phenomena in phase transition occur: for a relatively low adoption threshold of bigots, a change from first-order to second-order phase transition can be triggered by increasing the fraction of activists; for a relatively higher adoption threshold of bigots, a change from hybrid to second-order phase transition can be induced by varying the fraction of activists, decreasing mean degree or enhancing network heterogeneity. The theoretical predictions based on the suggested theory agree very well with the simulation results.