Abstract:

In general, the evolutionary time scale of group opinion formation can be considered significantly larger than the message propagation time scale on social media. However, this assumption does not hold for some extreme scenarios. Based on this, we established a noise threshold voter-UAU (unaware-aware-unaware) coupled model with an adjustable relative time scale between message propagation and opinion formation, and studied the collaborative interaction between two dynamics under different relative evolutionary rates and its effects on each other’s dynamical evolution . Both analyses based on mean field theory and Monte Carlo simulations demonstrate that a smaller time scale for message propagation relative to opinion formation is more favorable for the formation of a bistable phase, which is caused by the inherent differences between the two dynamics and their synergistic interaction. This study identified that the relative time scale between both dynamics not only affects the proportion of “positive” opinions in the final state, but also the critical basic reproduction number for message propagation that leads to a phase transition in the model. In particular, when the proportion of “positive” opinion is at different levels, their behaviors with respect to changes in the relative time scale between the two dynamics differ. When the proportion of “positive” opinions is high, a smaller time scale for message propagation leads to a higher proportion of “positive” opinions, and vice versa. This study addresses a gap in this field regarding the relative time scale’s impact on the dynamics of collaborative interaction coupling. Furthermore, it facilitates a more in-depth understanding of the profound influence of the relative time scale on the evolution dynamics of coupling dynamics.

Key words: message propagation, opinion formation, collaborative interaction, time scale