Rumor spreading occurs not only between two individuals but also among multiple individuals or influenced by groups. However, pairwise interactions in complex networks are insufficient to describe this process. In this study, we propose a rumor spreading model with higher-order interactions, in which the rumor propagation process is represented by simplicial complexes. By selecting the propagation coefficient and time delay as the threshold, the model shows richer dynamic behaviors, such as the bi-stability, discontinuous transition, forward bifurcation, backward bifurcation, Hopf bifurcation, and periodic oscillation. Besides, for exploring the collective behavior induced by rumors, the rumor synchronization model is first established by applying the adaptive feedback mechanism, which erects a theoretical bridge between rumor spreading and behavior diffusion. Moreover, an improved optimal control strategy considering system gains is performed to curb rumor diffusion. Numerical simulations suggest that rumor spreading models with higher-order interactions are more consistent with actual data than network-based ones. Our results may shed some light on comprehending higher-order interactions in rumor spreading and the coupling between rumor and behavior, and provide a promising approach to control rumors and irrational behaviors.

中文翻译：

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高阶交互的谣言传播与行为扩散模型的动态分析


谣言传播不仅发生在两个人之间，而且还发生在多个人之间或受群体影响。然而，复杂网络中的成对相互作用不足以描述这个过程。在本研究中，我们提出了一种具有高阶交互的谣言传播模型，其中谣言传播过程由单纯复合体表示。通过选择传播系数和时滞作为阈值，模型表现出更丰富的动态行为，如双稳态、不连续跃迁、前向分岔、后向分岔、Hopf分岔、周期振荡等。此外，为了探索谣言引发的集体行为，首次应用自适应反馈机制建立了谣言同步模型，在谣言传播和行为扩散之间架起了一座理论桥梁。此外，还采用考虑系统增益的改进最优控制策略来抑制谣言传播。数值模拟表明，具有高阶交互的谣言传播模型比基于网络的谣言传播模型更符合实际数据。我们的结果可能有助于理解谣言传播中的高阶相互作用以及谣言与行为之间的耦合，并为控制谣言和非理性行为提供一种有前途的方法。