双重社会强化谣言传播模型及稳定性分析

Rumor Spreading Model and Stability Analysis Considering the Double Social Reinforcements

谣言大规模扩散给社会造成了不良影响甚至严重危害,引发了学术界和政府的高度关注.通过分析群体正负双重社会强化效用对个体传播行为的影响,构建了谣言传播动力学模型,计算了平衡点和基本再生数,并运用Lyapunov函数法、Routh-Hurwitz稳定判据与复合矩阵等方法讨论了平衡点渐进稳定性.理论分析证明,当基本再生数不大于1时,谣言迅速消失,无谣言平衡点全局渐进稳定,否则谣言传播扩散,非零谣言平衡点全局渐进稳定.新浪微博仿真实验发现,在双重社会强化效用影响下,提高个体对谣言独立甄别能力有助于谣言由大规模扩散向迅速消失趋势转移;只有当抑制谣言传播的社会负强化足够大时,才能迅速终止谣言持续传播.

Rumor spreading has bad influence on our society and even leads serious damage. Researchers and governments have paid much attention to rumor spreading. This paper analyzes the effect of positive and negative double social reinforcements on the individual propagation behaviour, and proposes the rumor spreading dynamic model. The two equilibriums and the basic reproduction number are calculated. And then the asymptotical stability of the equilibriums is proved with the methods of Lyapunov functions, Routh-Hurwitz stability criterion and compound matrices. The theoretical analysis shows that if the basic reproduction number is not more than 1,the rumor will disappear quickly and the rumor-free equilibrium is globally asymptot- ically stable. Otherwise, the rumor will spread and the nonzero rumor equilibrium is globally asymptotically stable. Furthermore, the Sina Weibo numerical simulation results indicate that due to the effect of double social reinforcements, the enhancement of ability to identify the rumor independently is helpful for the tendency of rumor spreading process changing from the large-scale spreading to disappearing immediately. Lastly, it is also confirmed that only when the negative social reinforcement that suppresses rumor spreading is strong enough, the rumor spreading can be controlled.