一类具有媒体播报效应的谣言传播模型的定性分析
陈 华1,2

1.西安科技大学 能源学院,陕西 西安 710054; 2.延安大学 校办,陕西 延安 716000

谣言传播; 稳定性; Lyapunov函数; 媒体播报

Qualitative analysis of a rumor transmissionmodel with media coverage
CHEN Hua

(1.College of Energy Science and Engineering,Xi'an University of Science and Technology,Xi'an 710054,China; 2.President's Office,Yan'an University, Yan'an 716000,China)

rumor propagation; stability; lyapunov function; media broadcast

DOI: 10.13800/j.cnki.xakjdxxb.2016.0217

备注

为了准确刻画谣言传播机理,抑制谣言传播,文中研究了一类具有媒体播报效应的谣言传播模型。利用常微分方程稳定性理论,详细分析了系统平衡点的存在性及局部渐近稳定性; 通过比较定理证明了边界平衡点E0 (rumor-free equilibrium)的全局渐近稳定性,利用Lyapunov-LaSalle不变性原理给出了正平衡点E+ (rumor-endemic equilibrium)全局渐近稳定的充分条件。结论 表明,随着时间的推移,要么传谣者的数量趋于0,要么谣言持续,媒体报道对谣言传播的规模有一定影响。最后,通过数值模拟验证了媒体播报对谣言传播和控制的影响。

To understand the mechanism of the rumor propagation and inhibit the spread of rumors.We consider a rumor transmission model with media coverage.Based on the stability of ordinary differential equation,detailed qualitative analysis about the existence and local asymptotic stability of its equilibria is carried out.Using comparison theorem,we prove the globally asymptotic stability of the equilibrium E0 (rumor-free equilibrium).By use of Lyapunov-LaSalle invariant principle,we give some sufficient conditions which lead to the globally asymptotic stability of the equilibrium E+ (rumor-endemic equilibrium).We show that the number of infective individuals tends to zero as time evolves or the rumor persists.Furthermore,the numerical simulations show the impact of media coverage on the spread and control of rumor spreading.