The stability and hopf bifurcation of the multi-lingual rumor spreading model are mainly studied in this paper. A nonlinear inhibition mechanism is introduced to formulate an IS2R2 model with concerning the cross propagation in the multi-lingual environment. Next, the existence and stability of equilibrium points are analyzed systematically here. Meanwhile, choosing the key parameter and time delay of inhibition functions as bifurcation parameters, the characteristics of Hopf bifurcation are further displayed through certain critical values. Besides, an optimal control strategy involving inhibition functions is designed, and simulated via forward-backward sweep algorithm. Finally, the comparative analysis of various parameters in the numerical simulation is presented to justify our theoretical results.

本文主要研究多语言谣言传播模型的稳定性和hopf分叉问题。引入非线性抑制机制来构建IS2R2模型，该模型涉及多语言环境中的交叉传播。接下来，这里系统地分析了平衡点的存在性和稳定性。同时，选择抑制函数的关键参数和时延作为分岔参数，通过一定的临界值进一步展示Hopf分岔的特征。此外，设计了一种包含抑制函数的最优控制策略，并通过前向后向扫描算法进行了仿真。最后，对数值模拟中的各种参数进行了比较分析，以证明我们的理论结果。