Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments

Abstract In our modern world, the invention of Internet enables information as well as rumors to spread in an unprecedented speed. To investigate the spatio-temporal dynamics of rumor propagation, we propose a reaction-diffusion rumor spreading system with time delay as well as its variation on complex network models. Necessary conditions of the rumor-spreading equilibrium point and both diffusion and delay induced Turing bifurcation around the rumor-spreading equilibrium point are analysed. We further conduct mass numerical simulations on various network structures and non-networks models. The effects of constant and periodic diffusion terms as well as different incidence coefficients on the shapes of patterns are explored. Moreover, a type of spiral patterns on ‘LA4’ and ‘LA12’ networks with large time delay are discovered. Finally, we collect real data of information propagation on twitter, and determine values of parameters in our model to make fitting. The fitting curve matches real data well, which implies the validity of our model.