社交网络中谣言传播动力学研究

社交网络已成为谣言发酵与传播的主要媒介之一，因此有必要研究谣言在社交网络上的传播规律。本文结合时空滞后、空间扩散、媒体报道等因素对社交网络中谣言传播的影响，建立新的社交网络谣言时空传播模型。利用偏泛函微分方程理论，给出模型的稳定性以及发生Hopf分岔的判别条件。数值仿真显示时滞可以影响模型的收敛速度及改变模型的稳定性，同时，媒体对社交网络谣言的深度报道可以极大地减小网络中谣言传播者密度，并扩大系统的稳定区域。 最后，给出一些社交网络谣言传播控制策略。

Research on Rumor Spreading Dynamics in Social Networks

Social networks have been developed into one of the most important media for rumor fermentation and propagation, and it is necessary to disclose how the rumor spreads in social networks.Combined with the imports of spatial temporal delay, spatial diffusion and media coverage,a new delayed reaction diffusion rumor spreading model is developed. Applying the theory of partial functional differential equation, some stability and Hopf bifurcation conditions are given for the model. Examples are given to validate that delay can influence the convergence rate and the stability of the model, and media coverage benefits to reduce the density of rumor spreaders and expands the stability domain. Finally, some useful strategies forrumor spreading control in social networks are presented.