病毒式传播：基于共识驱动的采纳传播稳定性
Going Viral: Stability of Consensus-Driven Adoptive Spread
AI总结：
本文研究了复杂传染模型中采纳行为与社会强化效应的共进化，通过Lyapunov方法分析了全采纳和全不采纳状态的渐近稳定性，并给出了确定' flop'和' hit'状态稳定性的充分条件。
摘要：
在联网人群中，新产品传播通常被建模为传染病。然而，在'复杂'传染的情况下，这些模型无法捕捉到采纳行为中细致的动态社会强化效应。本文研究了一个复杂传染模型，允许采纳行为（建模为SIS传染病传播过程）与社会强化效应（建模为共识意见动态）之间的共进化。通过Lyapunov方法，提供了联合意见-采纳模型中全采纳和全不采纳平衡状态的渐近稳定性分析。在此过程中，提供了确定'flop'状态（没有人采纳产品且所有人对产品的意见最不利）和'hit'状态（所有人都采纳产品且他们的意见最有利）稳定性的充分条件。这些条件在更强的模型参数假设下扩展到有界信心意见动态。最后，数值模拟展示了模型的行为，反映了社会学文献中关于采纳行为的研究发现。
英文摘要：
The spread of new products in a networked population is often modeled as an epidemic. However, in the case of `complex' contagion, these models {do not capture nuanced, dynamic social reinforcement effects in adoption behavior}. In this paper, we investigate a model of complex contagion which allows a coevolutionary interplay between adoption, modeled as an SIS epidemic spreading process, and social reinforcement effects, modeled as consensus opinion dynamics. Asymptotic stability analysis of the all-adopt as well as the none-adopt equilibria of the combined opinion-adoption model is provided through the use of Lyapunov arguments. In doing so, sufficient conditions are provided which determine the stability of the `flop' state, where no one adopts the product and everyone's opinion of the product is least favorable, and the `hit' state, where everyone adopts and their opinions are most favorable. These conditions are shown to extend to the bounded confidence opinion dynamic under a stronger assumption on the model parameters. To conclude, numerical simulations demonstrate behavior of the model which reflect findings from the sociology literature on adoption behavior.
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