Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
School of Mathematical and Natural Sciences, Arizona State University, Phoenix, Arizona 85069-7100, USA.
Chaos. 2019 May;29(5):053106. doi: 10.1063/1.5090268.
Mathematical modeling is an important approach to research rumor propagation in online social networks. Most of prior work about rumor propagation either carried out empirical studies or focus on ordinary differential equation models with only consideration of temporal dimension; little attempt has been given on understanding rumor propagation over both temporal and spatial dimensions. This paper primarily addresses an issue related to how to define a spatial distance in online social networks by clustering and then proposes a partial differential equation model with a time delay to describing rumor propagation over both temporal and spatial dimensions. Theoretical analysis reveals the existence of equilibrium points, a priori bound of the solution, the local stability and the global stability of equilibrium points of our rumor propagation model. Finally, numerical simulations have analyzed the possible influence factors on rumor propagation and proved the validity of the theoretical analysis.
数学建模是研究在线社交网络中谣言传播的重要方法。之前关于谣言传播的大多数工作要么进行了实证研究，要么只关注仅考虑时间维度的常微分方程模型；很少有人试图理解时间和空间两个维度上的谣言传播。本文主要解决如何通过聚类在线社交网络中定义空间距离的问题，然后提出了一个具有时滞的偏微分方程模型来描述时间和空间两个维度上的谣言传播。理论分析揭示了我们的谣言传播模型的平衡点的存在、解的先验界、平衡点的局部稳定性和全局稳定性。最后，数值模拟分析了谣言传播的可能影响因素，验证了理论分析的有效性。
