Pattern study and parameter identification of a reaction-diffusion rumor propagation system with time delay

In this paper, a reaction-diffusion dynamic model with time delay is established under the background of network rumors, and the behavior of susceptible users and infected users in spreading rumors on the network is analyzed to help us study the mechanism of rumor propagation. Firstly, the Turing instability condition of delay approximate system is studied. Secondly, based on the amplitude equation method, the theoretical conditions of different patterns near Turing bifurcation point are given, and different types of Turing patterns are divided. Then, the accuracy of the theory is verified by numerical simulation under different parameters, and the effectiveness of the model is verified by Monte Carlo simulation. In addition, the effects of different networks and time-delay conditions on pattern formation are studied. Finally, in order to help the model apply to the actual situation, the parameter identification and optimization control of the system are carried out.