Heterogeneous behavioral adoption in multiplex networks - Xuzhen Zhu; Hui Tian; Xiaolong Chen; Wei Wang; Shimin Cai (New Journal of Physics, 2018)
Heterogeneity is found widely in populations, e.g. different individuals have diverse personalities and a different willingness to accept novel ideas or behaviors. Whereas population heterogeneity is rarely considered in studying the social contagions on complex networks, especially on multiplex networks. To explore the effect of population heterogeneity on the dynamics of social contagions, a novel model based on double-layer multiplex networks is proposed, in which information diffuses synchronously on the two layers, and each layer is assigned with different adoption thresholds. Meanwhile, populations are classified into the activists and conservatives according to their willingness to adopt new behaviors. To qualitatively understand the effect of population heterogeneity on social contagions, a generalized edge-based compartmental theory is proposed. Through rigorous theoretical analysis and extensive simulations, we find the activists in the two layers promote the adoption of behavior. More interestingly, the crossover phenomena in phase transition are found in the growth of the final adopted size when increasing the information transmission rate. When the proportion of activists is relatively large, the phase transition exhibits continuous pattern. Reducing the proportion of activists induces a hybrid transition, in which the final adoption size first grows continuously at the first threshold, and then increases discontinuously at the second threshold. In addition, we find that the network heterogeneity will change the crossover phenomena in phase transition.