Dynamic analysis of pattern and optimal control research of rumor propagation model on different networks

With the continuous development of network media, various rumors will inevitably appear in the process of information exchange and dissemination due to inadequate communication, and rumors are also easy to be more widely spread along the network public platform. At this time, it is particularly necessary to study and control information transmission. Based on the secondary transmission mechanism and the discrete characteristics of the network in real life, we use Laplacian matrix to build a reaction–diffusion model of information transmission. Then, in order to explore the distribution state of various types of people after perturbation is applied at the equilibrium point of the system, we use the correlated theory of Turing pattern to analyze the Turing instability of homogeneous network and heterogeneous network respectively to determine the necessary conditions for the emergence of Turing pattern. According to the specific situation of the appearance of different morphological patterns, the amplitude equation of the model is obtained by multi-scale analysis method. In addition, the theory is verified reasonably and effectively by numerical simulation. In view of different network structures, we first study the general pattern, and make a reasonable analysis of the propagation on the shortest path and the influence of government control. Second, in the simulation process of parameter identification based on optimal control theory, we can find that the algorithm type and network structure will affect the final convergence effect of parameters. Meanwhile, it can be found that connected with the selection of parameters, in order to achieve information control, we need both the intervention of government departments and the improvement of our own discrimination ability in real life. We can effectively control the crowd departure rate near the target value to achieve the ideal distribution state, which is of great significance for information control. Based on the above, we also have conducted a fitting analysis of the model combined with the relevant data of the number of epidemic-related tweets, which can explain the rationality of the model construction.