The probabilistic response of dual-layer stochastic complex propagation networks

The complex propagation structure consists of multiple interconnected subnetworks that exist widely in the real world. Taking the dual-layer network as an example, this study constructs an XY-ISR model to explore the stationary distribution and probability density function of the information propagation process. First, a stochastic information propagation model with external noise in a dual-layer network was established. Second, the existence, uniqueness of the solution and stationary distribution for the propagation model were analyzed using the stochastic analysis method. Third, we derive the exact expression of the probability density function near the quasi-equilibrium point by a standardized transformation method. Finally, the obtained results were verified through numerical simulations. The results show that the distribution feature can effectively characterize the risk level of information propagation. This provides a new perspective for the quantitative analysis and risk prediction of information dissemination, especially with potential application value in controlling the spread of public health misinformation.