Spatiotemporal dynamics analysis and parameter optimization of a network epidemic-like propagation model based on neural network method

In this paper, a reaction-diffusion model is established to study the dynamic behavior of rumor propagation. Firstly, we consider the existence of the positive equilibrium points. Then, we perform a stability analysis to study the conditions for the occurrence of Turing instability. Secondly, we use multiscale analysis to derive the expression of the amplitude equation. In the process of numerical simulation, the reality is considered. It shows that controlling the spread rate of rumor and the number of new Internet users have a great effect on curbing the spread of online rumor. Furthermore, it is proved that the analysis of amplitude equation plays a decisive role in the formation of Turing patterns. We also discuss the phenomenon of Turing patterns when the network structure changes and verify the rationality of the model by Monte Carlo method. Finally, we consider two methods based on statistical principle and convolutional neural network severally to identify the parameters of the reaction-diffusion system with Turing instability by using stable patterns. The statistical principle-based method offers superior accuracy, whereas the convolutional neural network-based approach significantly reduces recognition time and cuts down time costs.