Impact of the heterogeneity of adoption thresholds on behavior spreading in complex networks

Abstract

Individuals always exhibit distinct personal profiles ranging from education, social experiences to risk tolerance, which induces a vastly different response in the behavior spreading dynamics. To describe this phenomenon, a widely used method is to assign a distinct adoption threshold for each individual, which so far has eluded theoretical analysis. In this paper, we propose a behavior spreading model to describe the heterogeneity of individuals in adopting the behavior, in which the adoption threshold follows the Gaussian distribution. Based on the edge-based compartmental theory, the theoretical solutions of the behavior spreading size and the threshold are given for discontinuous and continuous phase transitions. Through theoretical analysis and extensive numerical simulations, the impact of the heterogeneity of adoption thresholds on behavior spreading is demonstrated, and we find that the phase transition depends on the mean and standard deviation of the adoption thresholds. For small values of the mean adoption threshold, the system exhibits a continuous phase transition. For large values of the mean adoption threshold, the phase transition is discontinuous (continuous) for the small (large) standard deviation of the adoption thresholds. There is a remarkable agreement between theoretical predictions and numerical simulations.