网络上观点的传播：Daley-Kendall模型中的收敛性、传播速度与模式
Propagation of opinions on a network. Convergence, spreading speed and patterns in the Daley-Kendall model
- Université Paris Cité, CNRS, Sorbonne Université, Laboratoire Jacques-Louis Lions (LJLL)（巴黎西岱大学、法国国家科学研究中心、索邦大学、雅克-路易·李翁斯实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究推广Daley-Kendall模型，建立无限图上的耦合微分方程系统，证明解收敛并给出传播速度估计，模拟显示考虑远距离个体时会出现局部观点采纳的“气泡”模式。
AI中文摘要：
我们研究了一个描述观点在网络上传播的社会传染模型。我们的模型是Daley和Kendall所引入模型的一个推广，由定义在无限图节点上的一组耦合微分方程组成。该建模受流行病学中SIR型模型的启发。关键思想在于，个体可以将其观点传播给邻居（如同流行病学模型中的情形），直到他们感知到该观点在自身邻域内已为人所知。在引入模型之后，我们分析了其解的长时间行为。我们证明了解是收敛的，并研究了其渐近平衡态。我们还建立了解在网络中传播速度的估计。这些结果给出了观点在社会网络中被采纳的速率及其传播速度的估计。我们还提供了数值模拟，表明该模型能够产生模式：当个体在估计观点是否已知时考虑了“足够远”的个体，我们观察到局部化的“气泡”出现，其中观点被采纳。
英文摘要：
We study a social contagion model describing the propagation of opinions across a network. Our model is a generalization of a model introduced by Daley and Kendall, and consists of a system of coupled differential equations set on the nodes of an infinite graph. The modeling is inspired by SIR-type models from epidemiology. The key idea is that individuals can transmit their opinion to their neighbors (as in epidemiological models), until they perceive that the opinion is already known in their neighborhood. After introducing the model, we analyze the long-time behavior of its solutions. We prove that the solutions converge and we study their asymptotic equilibrium. We also establish estimates on the speed of propagation of the solutions through the network. These results give estimates on the rate of adoption of the opinion and on its velocity in the social network. We also provide simulations that indicate that this model can give rise to patterns: when the individuals take into account individuals that are ''far enough'' in estimating whether or not the opinion is already known, then we observe the emergence of localized ''bubbles'' where the opinion is adopted.
