关键词: 谣言传播, 稳定性, 后向分支, Ｈｏｐｆ分支

Abstract: Based on the rumor spreading mechanism, considering the rumor recurrence caused by the interpersonal factor, this paper establishes a SEILR rumor spreading model, and studies the impact of this factor on rumor spreading. Firstly, the rumor spreading threshold R0 is given, and the stability of the rumor-free equilibrium point is analyzed when R0<1. Secondly, the existence of multiple equilibrium states is analyzed, and the condition of the occurrence of backward bifurcation is given. Then, the global asymptotic stability of the positive equilibrium point of the degenerate model is proved by constructing Lyapunov function. Finally, through numerical simulation, it is found that degenerate Hopf bifurcation appears and there are two limit cycles in the model, in which the large one is unstable and the small one is stable. The results show that the rumor recurrence caused by interpersonal factors can change the dynamic spreading trend of the rumors.