一类谣言传播模型的全局稳定性  

Global Stability of a Rumor Spreading Model

作　　者：吴韩超 张冬梅[1] 王定江[1] WU Han-chao;ZHANG Dong-mei;WANG Ding-jiang(College of Science,Zhejiang University of Technology,Hangzhou Zhejiang 310023 China)

机构地区：[1]浙江工业大学理学院,浙江杭州310023

出　　处：《生物数学学报》2020年第1期102-110,共9页Journal of Biomathematics

基　　金：浙江省自然科学基金(No.LY19A010013)

摘　　要：本文提出了一类具有媒体效应和标准传播率的谣言传播模型.基于谣言的基本再生数,分析了边界平衡点和正平衡点的存在性.利用Lyapunov-LaSalle不变集原理证明了边界平衡点的全局渐近稳定性,根据Routh-Hurwitz判据和广义Bendixson-Dulac定理证明了正平衡点的全局渐近稳定性.结果表明,媒体效应虽无法消除谣言,但能减小谣言传播的最终规模.数值例子验证了结论的有效性.A rumor spreading model with media coverage and standard incidence rate is established in this paper.The reproduction number of rumors is obtained,based on which,the existence of the boundary equilibrium and the positive equilibrium is analysed.The global stability of the boundary equilibrium is proved by using Lyapunov-LaSalle invariant principle,and the global stability of the positive equilibrium is proved according to Routh-Hurwitz criterion and the generalized Bendixson-Dulac theorem.It is concluded that although the media coverage can’t eliminate rumors,it can control the rumor spreading.Examples illustrate the effectiveness of the proposed results.

关 键 词：谣言传播模型 基本再生数 广义Bendixson判据 稳定性 

分 类 号：G206[文化科学—传播学]