Effects of heterogeneous adoption thresholds on contact-limited social contagions

Abstract

Limited contact capacity and heterogeneous adoption thresholds have been proven to be two essential characteristics of individuals in natural complex social systems, and their impacts on social contagions exhibit complex nature. With this in mind, a heterogeneous contact-limited threshold mode is proposed, which adopts one of four threshold distribution, namely Gaussian distribution, log-normal distribution, exponential distribution and power-law distribution. The heterogeneous edge-based compartmental theory is developed for theoretical analysis, and the calculation methods of the final adoption size and outbreak threshold are given theoretically. Many numerical simulations are performed on the ER and SF networks to study the impact of different forms of threshold distribution on hierarchical spreading process, the final adoption size, the outbreak threshold and the phase transition in contact-limited propagation networks. We find that the spreading process of social contagions is divided into three distinct stages. Moreover, different threshold distributions cause different spreading processes, especially for some threshold distributions, there is a change from a discontinuous first-order phase transition to a continuous second-order phase transition. Further, we find that changing the standard deviation of different threshold distributions will cause the final adoption size and outbreak threshold to change, and finally tend to be stable with the increase of standard deviation.

Analysis of Influence of Behavioral Adoption Threshold Diversity on Multi-Layer Network

“…The A-layer and B-layer networks are two separate networks, which are coupled to each other by the same individual, and the individual possesses different adoption thresholds on different layers. The scholars proposed a generalized Susceptible-Adopted-Recovered (SAR) [ 29 , 30 ] model to represent the information propagation mechanism in the two-layer networks, as illustrated in Figure 1 a. In the SAR model, each node in the network has three different states, namely, the susceptible state, adopted state, and recovered state, corresponding to the S-state, A-state, and R-state, respectively.…”

SAR dynamical mechanism affected by diminishing marginal effect based on personal fashion psychology on multi-layer contacted network

“…To examine the effect of personal heterogeneous contact on social communication, Zhao et al [24] constructed a heterogeneous behavioral model. Nie et al [25] studied the effect of complex contacts on behavioral diffusion in population networks. Therefore, a social acceptance of individual must be manifested in his ability to communicate, given the impact of the limited interactions of individual on reality.…”