Global dynamic analysis of a multi-platform rumor propagation model based on the information cocoons

In the digital age, rumor dissemination tends to be diverse and complex. To further analyze its mechanism, this article focuses on the phenomenon of information cocoons, quantifying it as individual opinion intensity and echo chamber intensity. We introduce a general occurrence function to improve the classical SIR rumor propagation model, providing a new perspective for studying new rumor propagation mechanisms. Firstly, a rumor propagation model under dual social platforms is constructed, and the Lyapunov stability theory is used to prove the global asymptotic stability of the equilibrium point. Subsequently, the model is extended to multiplatform scenarios to analyze the global asymptotic stability of propagation dynamics dominated by the basic reproduction number at equilibrium points. To effectively suppress the spread of rumors, a real-time optimization control strategy is implemented to minimize control costs while ensuring that the spread of rumors is contained within the expected time. Finally, numerical simulations are given to validate the effectiveness of the model and explore the impact of different factors on propagation. Further research has shown that the lower the intensity of user opinions and the stronger the echo chamber effect, the slower the disappearance of rumor spreaders and the higher the difficulty of platform control. This article provides theoretical basis and control ideas for rumor management.