时滞在线社交网络谣言传播模型的动力学分析

Dynamic Analysis of Rumor Propagation Model in Online Social Networks with Time Delay

摘要: 本文考虑了在谣言传播过程中，政府干预带来的时滞效应，建立了时滞在线社交网络谣言传播模型。运用常微分方程稳定性的相关知识讨论了正平衡点E^*的存在性以及稳定性问题，并证明得到了其发生Hopf分岔的判别条件。发现在满足相应条件下，当时滞不超过临界值时，正平衡点E^*局部渐进稳定，当超出临界值时，正平衡点E^*将由稳定变为不稳定。最后，通过数值来仿真模拟正平衡点的局部稳定性，并验证理论的正确性。

Abstract: This paper considers the time delay effect brought by government intervention in the process of rumor propagation and establishes a time-delayed online social network rumor propagation model. By using knowledge related to the stability of ordinary differential equations, the existence and stability of the positive equilibrium point are discussed, and the discriminant conditions for Hopf bifurcation are proved. It is found that under the corresponding conditions, when the time delay does not exceed the critical value, the positive equilibrium point is locally asymptotically stable, and when it exceeds the critical value, the positive equilibrium point changes from stable to unstable. Finally, numerical simulations are conducted to verify the local stability of the positive equilibrium point and validate the correctness of the theory.