社交网络中的谣言传播模型与全局动力学分析

传统的谣言传播模型不考虑人群评价对谣言传播的影响,但随着弹幕、评论点赞、评论排序等新机制的广泛应用,人群评论对谣言传播产生了不可忽视的影响.基于上述情况,本文提出一类新型的基于评价机制的ICST谣言传播模型,该模型将人群细化为无知者（I）、评论者（C）、传播者（S）和静默者（T）四类.在验证平衡点存在性的基础上给出了谣言传播阈值R₀,并依据模型的网络结构构造李雅普诺夫函数证明平衡点的全局稳定性.最后,设计仿真算法验证了理论结果的正确性.

Global dynamic analysis of a rumor spreading model in online social networks

The influence of comments is ignored in traditional rumor spreading models,however,it has recently become an important factor,especially with the wide and diversified application of comments in online social networks,such as bullet-screen,like button,and comment ranking.To address this,we propose an ICST rumor spreading model taking comment mechanism into account,which classifies the population involved in rumor spreading processes into ignorants (I),commentators (C),spreaders (S),and stiflers (T).The existence of the equilibriums is proved,based on which the sharp threshold of rumor propagation is given.Global stability of the information-elimination equilibrium and the information-prevailing equilibrium is proved by constructing Lyapunov function.Numerical examples are given to verify the above theoretical analysis.