Bifurcation and control of a delayed reaction-diffusion rumor spreading model with medium mechanism

Rumor spreading in online social networks has gradually become a hot topic in the public. In this paper, we present a delayed reaction-diffusion rumor spreading model with consideration of medium mechanism in online social networks. By choosing the delay as a bifurcation parameter, the local stability of the equilibrium points are discussed and the conditions of Hopf bifurcation are obtained. Meanwhile, some numerical simulations are also given to illustrate our theoretical results. Furthermore, in consideration of the impact of authorities' actions on controlling rumor spreading, we introduce a time-delay state feedback controller to describe authorities' actions and finally an example vividly displays that a negative feedback control will reduce system stability and a positive feedback control can increase system stability.