一般情况下, 群体意见形成的演化时间尺度可被认为远远大于社交媒体上消息传播的时间尺度. 但是在某些极端场景中, 以上的假设却并不成立. 基于此, 建立了一个消息扩散和意见形成之间的相对时间尺度可调的噪声阈值投票者-UAU (unaware-aware-unaware)模型, 并研究了不同的相对演化速度下社交媒体上的消息传播与人群意见形成之间的相互协同作用对彼此演化动态的影响. 基于平均场理论(mean-field theory, MFT)的分析和Monte Carlo模拟都表明, 相较于意见形成, 消息传播的时间尺度越小越有利于双稳态相的形成, 这是两种动力学的本征差异和它们之间的协同相互作用造成的. 研究发现, 两种动力学间的相对时间尺度不仅影响终态的“正”意见比例, 还影响导致模型发生相变的临界基本再生数的大小; 特别是当“正”意见比例处于不同的水平时, 其随着两种动力学相对时间尺度的变化行为是不同的, 当“正”意见比例较高时, 消息传播的时间尺度相对于意见形成越小则“正”意见比例越大, 反之则相反. 研究填补了相对时间尺度对于协同相互作用耦合动力学影响这一研究领域的空白, 有助于人们更加深入地理解相对时间尺度对耦合动力学演化动态的影响.

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.