【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.更多还原

【Abstract】 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.更多还原