Pattern dynamics analysis of a reaction-diffusion network propagation model

In this paper, considering the spatial propagation behavior of Internet rumor, we propose a new reaction-diffusion rumor propagation model with time delay in social networks. Based on this, we discuss the stability conditions at the equilibrium point and analyze the Turing instability for the approximation propagation system. Simultaneously, the amplitude equations for the approximation system are derived by multiscale analysis. We use numerical simulation to compare the effect of parameter size, period, and time delay on the patterns. Moreover, we compare the different reactivity of the system in the WS networks and the BA networks. Finally, we plot the corresponding amplitude equations patterns by controlling the parameters and verify the correctness of the theoretical results.