The dynamic analysis of the rumor spreading and behavior diffusion model with higher-order interactions

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.